equations and problem solving

(For help, go to Lesson 1-1.)

ALGEBRA 1 LESSON 4-8ALGEBRA 1 LESSON 4-8

Write a variable expression for each situation.

1. value in cents of q quarters

2. twice the length

3. number of miles traveled at 34 mi/h in h hours

4. weight of 5 crates if each crate weighs x kilograms

5. cost of n items at $3.99 per item

Equations and Problem Solving

4-8

Solutions

1. value in cents of q quarters: 25q

2. twice the length : 2

3. number of miles traveled at 34 mi/h in h hours: 34h

4. weight of 5 crates if each crate weighs x kilograms: 5x

5. cost of n items at $3.99 per item: 3.99n

Equations and Problem SolvingALGEBRA 1 LESSON 4-8ALGEBRA 1 LESSON 4-8

4-8

An airplane left an airport flying at 180 mi/h. A jet that flies at

330 mi/h left 1 hour later. The jet follows the same route as the

airplane on parallel altitudes. How many hours will it take the jet to

catch up with the airplane?

Aircraft Rate Time Distance Traveled

Airplane 180 t 180t

Jet 330 t – 1 330(t – 1)

Define: Let t = the time the airplane travels.

Then t – 1 = the time the jet travels.


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Relate: distance traveled equals distance traveledby airplane by jet

Write: 180 t = 330( t – 1 )

180t = 330(t – 1)180t = 330t – 330 Use the Distributive Property.

180t – 330t = 330t – 330 – 330t Subtract 330t from each side.

–150t = –330 Combine like terms.


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(continued)

= Divide each side by –150.–150t–150

–330–150

t = 2 Simplify.15

t – 1 = 1 15

The jet will catch up with the airplane in 1 h.15

Suppose you hike up a hill at 4 km/h. You hike back down at

6 km/h. Your hiking trip took 3 hours. How long was your trip up the

hill?

Define: Let x = time of trip uphill.

Then 3 – x = time of trip downhill.

Relate: distance uphill equals distance downhill

Part of hike Rate Time Distance hiked

Uphill 4 x 4x

Downhill 6 3 – x 6(3 – x)

Write: 4 x = 6( 3 – x )


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4x = 6(3 – x)

4x = 18 – 6x Use the Distributive Property.

4x + 6x = 18 – 6x + 6x Add 6x to each side.

10x = 18 Combine like terms.


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(continued)

= Divide each side by 10.10x10

1810

x = 1 Simplify.45

Your trip uphill was 1 h long.45

Two jets leave Dallas at the same time and fly in opposite

directions. One is flying west 50 mi/h faster than the other. After

2 hours, they are 2500 miles apart. Find the speed of each jet.

Define: Let x = the speed of the jet flying east.

Write: 2 x + 2( x + 50 ) = 2500

Then x + 50 = the speed of the jet flying west.

Relate: eastbound jet’s plus westbound jet’s equals the total distance distance distance

Jet Rate Time Distance Traveled

Eastbound x 2 2x

Westbound x + 50 2 2(x + 50)


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2x + 2(x + 50) = 2500

2x + 2x + 100 = 2500 Use the Distributive Property.

4x + 100 = 2500 Combine like terms.

4x + 100 – 100 = 2500 – 100 Subtract 100 from each side.4x = 2400 Simplify.

x = 600

x + 50 = 650

The jet flying east is flying at 600 mi/h. The jet flying west is flying at 650 mi/h.


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(continued)

= Divide each side by 4.4x4

24004

1. The sum of three consecutive integers is 117. Find the integers.

2. You and your brother started biking at noon from places that are 52 mi apart. You rode toward each other and met at 2:00 p.m. Your brother’s average speed was 4 mi/h faster than your average speed. Find both speeds.

3. Joan ran from her home to the lake at 8 mi/h. She ran back home at 6 mi/h. Her total running time was 32 minutes. How much time did it take Joan to run from her home to the lake?

38, 39, 40

your speed: 11 mi/h; brother’s speed: 15 mi/h

about 13.7 minutes


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