story problems ii

STORY PROBLEMS II

THE “REALLY TOUGH STUFF”

General Directions for d = rt problems

1. Read the problem carefully.2. Ask yourself, “What am I trying to

find.”3. Determine what kind of a problem

it is.4. Write your equation and solve5. Ask yourself, “Did I answer the

question asked?”

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe? What am I trying to find?How long does it take the MOTORBOAT to catch the canoe. In other words, how long is the motorboat on the water?

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe? This problem contains speed (rate) and

time.

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe? Use d = rt Make a table of the information.

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?

Rate Time DistanceCanoeMotorboat

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?

Rate Time DistanceCanoe 12Motorboat

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?

Rate Time DistanceCanoe 12Motorboat 21

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?

Rate Time DistanceCanoe 12 tMotorboat 21

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?

Rate Time DistanceCanoe 12 tMotorboat 21 t - 2

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?

Rate Time DistanceCanoe 12 t 12tMotorboat 21 t - 2

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?

Rate Time DistanceCanoe 12 t 12tMotorboat 21 t - 2 21(t - 2)

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe? The motorboat has caught the canoe

(same direction) The distances traveled by both must be

the same. Set the two distances equal to each

other and solve.

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?

12 𝑡=21(𝑡−2)

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?

12 𝑡=21(𝑡−2)

12 𝑡=21𝑡−42

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?

12 𝑡=21(𝑡−2)

12 𝑡=21𝑡−42−9𝑡=−42

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?

12 𝑡=21(𝑡−2)

12 𝑡=21𝑡−42−9𝑡=−42

𝑡=−42−9

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?

)

12 𝑡=21𝑡−42−9𝑡=−42

𝑡=−42−9 =4.6

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?

)

12 𝑡=21𝑡−42−9𝑡=−42

𝑡=−42−9 =4.6

You can convert your answer to hours and minutes if you like.

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?

12 𝑡=21¿

12 𝑡=21𝑡−42−9𝑡=−42

𝑡=−42−9 =4.6

You can convert your answer to hours and minutes if you like.The time you have found is the time for the canoe. You were not asked to find that. Find the motorboat’s time.

A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?

12 𝑡=21¿

12 𝑡=21𝑡−42−9𝑡=−42

𝑡=−42−9 =4 .6It takes the motorboat 2 hours and 40 minutes to catch the canoe. Or you can just leave it hours.

You can convert your answer to hours and minutes if you like.The time you have found is the time for the canoe. You were not asked to find that. Find the motorboat’s time.

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4 km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you arrive at the top of the hill? This problem contains rate and time

(but it is given as “clock” time.) If you go to a location, then come

back, you have a “round trip” situation

In a round trip, the distances are equal.

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill? Make a table. Add a column for the “clock” time.

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill?

Rate Time Distance

Clock

UpDown

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill?

Rate Time Distance

Clock

Up 4Down

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill?

Rate Time Distance

Clock

Up 4Down 6

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill?

Rate Time Distance

Clock

Up 4 tDown 6

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill?

Rate Time Distance

Clock

Up 4 tDown 6 3 - t

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill?

Rate Time Distance

Clock

Up 4 t 4tDown 6 3 - t

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill?

Rate Time Distance

Clock

Up 4 t 4tDown 6 3 - t 6(3 – t)

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill?

Rate Time Distance

Clock

Up 4 t 4t 9:00 amDown 6 3 - t 6(3 – t)

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill?

Rate Time Distance

Clock

Up 4 t 4t 9:00 amDown 6 3 - t 6(3 – t) ????

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill? 4 𝑡=6 (3−𝑡)

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill? 4 𝑡=6 (3−𝑡)4 𝑡=18−6 𝑡

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill? 4 𝑡=6 (3−𝑡)4 𝑡=18−6 𝑡10 𝑡=18

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill? 4 𝑡=6 (3−𝑡)4 𝑡=18−6 𝑡10 𝑡=18

𝑡=1810

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill? 4 𝑡=6 (3−𝑡)4 𝑡=18−6 𝑡10 𝑡=18

𝑡= 1810=1.8hours

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill? 4 𝑡=6 (3−𝑡)4 𝑡=18−6 𝑡10 𝑡=18

𝑡= 1810=1.8hours

This does NOT answer the question asked. This is how long it takes to get to the top of the hill, not AT WHAT TIME?

Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4

km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you

arrive at the top of the hill? 4 𝑡=6 (3−𝑡)4 𝑡=18−6 𝑡10 𝑡=18

𝑡=1810=1.4 hours

This does NOT answer the question asked. This is how long it takes to get to the top of the hill, not AT WHAT TIME?

If you left at 9:00 am, and it took 1.8 hours (or 1 hour 48 minutes), then you arrived at the top of the hill at 10:48 am.

Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the jets are 1250 miles apart. Find the speed of each jet.

The jets are flying in “opposite directions.”

To solve an opposite direction problem, ADD the distances traveled to find the distance apart.

Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the

jets are 1250 miles apart. Find the speed of each jet.

Make a table.

Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the

jets are 1250 miles apart. Find the speed of each jet.

Rate Time DistanceWestboundEastbound

Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the

jets are 1250 miles apart. Find the speed of each jet.

Rate Time DistanceWestbound r + 25Eastbound

Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the

jets are 1250 miles apart. Find the speed of each jet.

Rate Time DistanceWestbound r + 25Eastbound r

Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the

jets are 1250 miles apart. Find the speed of each jet.

Rate Time DistanceWestbound r + 25 2Eastbound r

Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the

jets are 1250 miles apart. Find the speed of each jet.

Rate Time DistanceWestbound r + 25 2Eastbound r 2

Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the

jets are 1250 miles apart. Find the speed of each jet.

Rate Time DistanceWestbound r + 25 2 2(r+25)Eastbound r 2

Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the

jets are 1250 miles apart. Find the speed of each jet.

Rate Time DistanceWestbound r + 25 2 2(r+25)Eastbound r 2 2r

Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the

jets are 1250 miles apart. Find the speed of each jet.

Rate Time DistanceWestbound r + 25 2 2(r+25)Eastbound r 2 2r

2𝑟+2 (𝑟+25 )=1250

Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the

jets are 1250 miles apart. Find the speed of each jet.

Rate Time DistanceWestbound r + 25 2 2(r+25)Eastbound r 2 2r

2𝑟+2 (𝑟+25 )=1250

2𝑟+2𝑟+50=1250

Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the

jets are 1250 miles apart. Find the speed of each jet.

Rate Time DistanceWestbound r + 25 2 2(r+25)Eastbound r 2 2r

2𝑟+2 (𝑟+25 )=1250

2𝑟+2𝑟+50=12504𝑟+50=1250

Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the

jets are 1250 miles apart. Find the speed of each jet.

Rate Time DistanceWestbound r + 25 2 2(r+25)Eastbound r 2 2r

2𝑟+2 (𝑟+25 )=1250

2𝑟+2𝑟+50=12504𝑟+50=1250

4𝑟=1200

Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the

jets are 1250 miles apart. Find the speed of each jet.

Rate Time DistanceWestbound r + 25 2 2(r + 25)Eastbound r 2 2r

2𝑟+2 (𝑟+25 )=1250

2𝑟+2𝑟+50=12504𝑟+50=1250

4𝑟=1200𝑟=300

Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the

jets are 1250 miles apart. Find the speed of each jet.

Rate Time DistanceWestbound r + 25 2 2(r +25)Eastbound r 2 2r

2𝑟+2 (𝑟+25 )=1250

2𝑟+2𝑟+50=12504𝑟+50=1250

4𝑟=1200𝑟=300

The rate (r) is the rate of the eastbound jet. Therefore, the westbound jet is flying at 325 mph.

Wrap-up There are three type of problems. Same direction Round-trip Opposite direction In same direction and round-trip

problems, you set the distances equal to each other.

In opposite direction, you add the distances together.

Assignment2.5B: 10 - 24