Beginning Algebra, 11th Edition

Write a system of equations for each problem, and then solve the system. See Example 4.

31.Two trains start from towns 495 mi apart and travel toward each other on parallel tracks.

They pass each other 4.5 hr later. If one train travels 10 mph faster than the other, find the

rate of each train.

32.Two trains that are 495 mi apart travel toward each other. They pass each other 5 hr later.

If one train travels half as fast as the other, what are their rates?

33.Kansas City and Denver are 600 mi apart.

Two cars start from these cities, traveling

toward each other. They pass each other

after 6 hr. Find the rate of each car if one

travels 30 mph slower than the other.

34.Toledo and Cincinnati are 200 mi apart. A car

leaves Toledo traveling toward Cincinnati, and

another car leaves Cincinnati at the same time,

traveling toward Toledo. The car leaving Toledo

averages 15 mph faster than the other car, and

they pass each other after 1 hr and 36 min. What

are the rates of the cars?

35. RAGBRAI®, the Des Moines Register’s
    Annual Great Bicycle Ride Across Iowa, is
    the longest and oldest touring bicycle ride in
    the world. Suppose a cyclist began the 471 mi
    ride on July 20, 2008, in western Iowa at the
    same time that a car traveling toward it left
    eastern Iowa. If the bicycle and the car met
    after 7.5 hr and the car traveled 35.8 mph
    faster than the bicycle, find the average rate
    of each. (Source:www.ragbrai.com)

36.In 2008, Atlanta’s Hartsfield Airport was the world’s busiest. Suppose two planes leave

Hartsfield at the same time, one traveling east and the other traveling west. If the planes

are 2100 mi apart after 2 hr and one plane travels 50 mph faster than the other, find the

rate of each plane. (Source:Airports Council International.)

37.A boat takes 3 hr to go 24 mi upstream. It can go

36 mi downstream in the same time. Find the

rate of the current and the rate of the boat in still

water if the rate of the boat in still water and

the rate of the current.

(Hint:Because the current pushes the boat when it is going downstream, the rate of the

boat downstream is the sumof the rate of the boat and the rate of the current. The current

slows down the boat when it is going upstream, so the rate of the boat upstream is the

differenceof the rate of the boat and the rate of the current.)

38.It takes a boat hr to go 12 mi downstream,

and 6 hr to return. Find the rate of the boat in

still water and the rate of the current. Let the

rate of the boat in still water and the rate of

the current.

y=

x=

(^1 12)
y=
x=

280 CHAPTER 4 Systems of Linear Equations and Inequalities

Denver Kansas City

600 mi

Rate: x Rate: x + 30

Pennsylvania

Kentucky West Virginia

Indiana

Ohio

200 mi

Michigan

Toledo Lake ErieLake Erie

Cincinnati

Missouri

Valley

Harlan

JeffersonAmes Tama-Toledo Tipton

North

Liberty

Le Claire

rt d

Downstream 3

Upstream x-y 3

x+y 31 x+y 2

rt d

Downstream

Upstream x-y 6

3

x+y 2

30.Jasmine Vazquez, who works at a delicatessen, is preparing a cheese tray using some

cheeses that sell for $8 per lb and others that sell for $12 per lb. How many pounds of

cheese at each price should she use in order for the cheeses on the tray to weigh a total of

56 lb and sell for $10.50 per lb?

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