Tool BagFormulas, equations,Vocabulary, etc.

Here’s How…Notes & Examples

Title: Name Date Period

5-2 (Part 3): Rates Using Bar Models

Objective To use bar models to determine rates.Example #1

A car leaves Oakland for Las Vegas traveling an average of 40 mph. Two hours later, a truck leaves the same place in Oakland for Las Vegas at 60 mph. How long will it be beforethe truck overtakes the car?

Bar Model Method

401

402

403

404

The time it takes the truck to overtake the car is 4 hours....

Overtake/Catch-Up Problem

405

4060

Hours

Distance80 120 160 200 2400 40

Car:

00

00

601

602

603

6040

Hours

Distance0 60 120 180 2400 0

Truck:

Tool BagFormulas, equations,Vocabulary, etc.

Here’s How…Notes & Examples

Title: Name Date Period

5-2 (Part 3): Rates Using Bar Models

Equation Method40(x+2) = 60x

The time it takes the truck to overtake the car is 4 hours....

40x + 80 = 60x40x – 40x + 80 = 60x – 40x

80 = 20x

You Try A sailboat leaves San Francisco for Los Angeles at 30 mph. A motorboat leaves the same place two hours later in San Francisco for Los Angeles at 50 mph. How long will it take until the motorboat catches up to the sailboat?

Let x = the time it takes the truck to overtake the car.

8020

20x20

=

4 = x

Tool BagFormulas, equations,Vocabulary, etc.

Here’s How…Notes & Examples

Title: Name Date Period

5-2 (Part 3): Rates Using Bar Models

Example #2

A car leaves San Francisco for Anaheim traveling an average of 65 mph. At the same time, another car leaves Anaheim for San Francisco traveling an average of 60 mph. If it is 500 miles between San Francisco and Anaheim, how long until the two cars meet?

Bar Model Method

60+651 2 3 4

It will take the cars 4 hours to meet....

“Meet” Problem

0Hours

Total Miles Driven250 375 5000 125

Let x = the time until the two cars meet.

60+65 60+65 60+65

Tool BagFormulas, equations,Vocabulary, etc.

Here’s How…Notes & Examples

Title: Name Date Period

5-2 (Part 3): Rates Using Bar Models

Equation Method65x + 60x = 500

It will take the cars 4 hours to meet....

125x = 500

You Try Sarah leaves her house for her friend’s house walking at 4 mph. At the same time, her friend Jessica leaves her housefor Sarah’s house walking at 3 mph. If they live 21 miles apart,how long will it take until Sarah and Jessica meet?

Let x = the time until the two cars meet.

125x125

500125

=

x = 4