Intermediate Algebra (11th edition)

Step 3 Write a system of equations.The car travels 8 km per hr faster than the

truck. Since the two rates are xand y,

(1)

Both vehicles travel for the sametime, so the times must be equal.

Time for car Time for truck

This is not a linear equation. However, multiplying each side by xygives

(2)

which is linear. The system to solve consists of equations (1) and (2).

(1)

(2)

Step 4 Solvethe system by substitution. Replace xwith in equation (2).

(2)

Let

Distributive property

Subtract 225y.

y= 72 Divide by 25.

25 y= 1800

250 y= 225 y+ 1800

250 y= 2251 y+ 82 x=y+8.

250 y= 225 x

y+ 8

250 y= 225 x

x=y+ 8

250 y= 225 x,

250

x

=

225

y

x=y+ 8.

238 CHAPTER 4 Systems of Linear Equations

drt

Car 250 x

Truck 225 y^225 y

250

x

NOW TRY
EXERCISE 4
Vann and Ivy Sample are
planning a bicycle ride to
raise money for cancer re-
search. Vann can travel 50 mi
in the same amount of time
that Ivy can travel 40 mi.
Determine both bicyclists’
rates, if Vann’s rate is 2 mph
faster than Ivy’s.

As in Example 3,a table helps organize the information. Fill in the distance

for each vehicle, and the variables for the unknown rates.

To find the expressions for time,

we solved the distance formula

d=rtfor t. Thus, rd=t.

Because the value of xis

Step 5 State the answer.The rate of the car is 80 km per hr, and the rate of the

truck is 72 km per hr.

Step 6 Check.

Truck: t=

d

r

=

225

72

= 3.125

Car: t=

d

r

=

250

80

= 3.125

x=y+8, 72 + 8 =80.

Be sure to use

parentheses

around y+8.

Since 80 is 8 greater than 72, the conditions of the problem are satisfied.

NOW TRY

OBJECTIVE 5 Solve problems with three variables by using a system of

three equations.

Times are

equal.

If an application requires finding threeunknown quantities, we can use a

system of threeequations to solve it. We extend the method used for two

unknowns.

PROBLEM-SOLVING HINT

NOW TRY ANSWER

4. Vann: 10 mph; Ivy: 8 mph