Solving a Proportion Involving Rates

Jodie Fry’s car uses 10 gal of gasoline to travel 210 mi. She has 5 gal of gasoline in the

car, and she wants to know how much more gasoline she will need to drive 640 mi. If

we assume the car continues to use gasoline at the same rate, how many more gallons

will she need?

Step 1 Readthe problem.

Step 2 Assign a variable.Let the additional number of gallons of gas needed.

Step 3 Write an equation.To get an equation, set up a proportion.

Step 4 Solve.We could multiply both sides by the LCD Instead we

use an alternative method that involves cross products:

For to be true, the cross products and must be equal.

ad b c

If then

Multiply; distributive property

Subtract 1050.

Divide by 210. Round to the nearest tenth.

Step 5 State the answer.Jodie will need about 25.5 more gallons of gas.

Step 6 Check.The 25.5 gal plus the 5 gal equals 30.5 gal.

and

Since the rates are equal, the solution is correct. NOW TRY

10

210

L0.048

30.5

640

L0.048

25.5Lx

5350 = 210 x

6400 = 1050 + 210 x

10 # 640 = 21015 + x (^2) ba=dc , ad=bc.

=

ad bc

a

b =

c

d

10 # 21 #64.

gallons

miles

10

210

=

5 +x

640

gallons

miles

x=

EXAMPLE 5

398 CHAPTER 7 Rational Expressions and Functions

NOW TRY
EXERCISE 5
Clayton’s SUV uses 28 gal of
gasoline to drive 500 mi. He
has 10 gal of gasoline in the
SUV, and wants to know how
much more gasoline he will
need to drive 400 mi. If we
assume the car continues to
use gasoline at the same rate,
how many more gallons will
he need?

OBJECTIVE 4 Solve applications about distance, rate, and time. We intro-

duced the distance formula in Section 2.2.Using this formula,

Rate is the ratio of distance to time, or

Time is the ratio of distance to rate, or t= dr.

r= dt.

d= rt

Solving a Problem about Distance, Rate, and Time

A paddle wheeler goes 10 mi against the

current in a river in the same time that it

goes 15 mi with the current. If the rate of

the current is 3 mph, find the rate of the

boat in still water.

Step 1 Readthe problem.

Step 2 Assign a variable.Let

of the boat in still water.

Traveling againstthe current slows the boat down, so the rate of the boat is

the differencebetween its rate in still water and the rate of the current — that

is, 1 x- 32 mph.

x=the rate

EXAMPLE 6

NOW TRY ANSWER
5.12.4 more gallons