Beginning Algebra, 11th Edition

SECTION 2.7 Further Applications of Linear Equations^145

Solving a Motion Problem

Two planes leave Memphis at the same time. One heads south to New Orleans. The

other heads north to Chicago. The Chicago plane flies 50 mph faster than the

New Orleans plane. In hr, the planes are 275 mi apart. What are their rates?

Step 1 Readthe problem carefully.

Step 2 Assign a variable.

Let the rate of the slower plane.

Then the rate of the faster plane.

Step 3 Write an equation.As FIGURE 17shows, the planes are headed in opposite

directions. The sumof their distances equals 275 mi.

Step 4 Solve. Multiply by 2.

Combine like terms.

Subtract 50.

Divide by 2.

Step 5 State the answer.The slower plane (headed south) has a rate of 250 mph.

The rate of the faster plane is

Step 6 Check.Verify that^12 12502 +^12 13002 = 275 mi. NOW TRY

250 + 50 =300 mph.

r = 250

2 r = 500

2 r+ 50 = 550

r+ 1 r+ 502 = 550

1

2

r+

1

2

1 r+ 502 = 275

r+ 50 =

r=

1

2

EXAMPLE 7

Faster

plane

Slower

plane

N

S

Chicago

New Orleans

Memphis

(^12) r
(^12) (r + 50)
FIGURE 17
NOW TRY
EXERCISE 7
Two cars leave a parking lot at
the same time, one traveling
east and the other traveling
west. The westbound car travels
6 mph faster than the eastbound
car. In hr, they are 35 mi
apart. What are their rates?
1
4
Rate Time Distance
Slower plane r
Faster plane r+ 50 12 121 r+ 502
1
2 r
1
2
NOW TRY ANSWER

7. 67 mph; 73 mph

Sum is 275 mi.

Complete solution available
on the Video Resources on DVD

2.7 EXERCISES

Answer each question. See Example 1 and the Problem-Solving Hint preceding Example 4.

1.How much pure alcohol is in 150 L of a 30% alcohol solution?

2.How much pure acid is in 250 mL of a 14% acid solution?

3.If $25,000 is invested for 1 yr at 3% simple interest, how much interest is earned?

4.If $10,000 is invested for 1 yr at 3.5% simple interest, how much interest is earned?

5.What is the monetary value of 35 half-dollars?

6.What is the monetary value of 283 nickels?

Concept Check Solve each percent problem. Remember that base rate percentage.

7.The population of New Mexico in 2007 was about 1,917,000, with 44.4% Hispanic. What

is the best estimate of the Hispanic population in New Mexico? (Source:U.S. Census

Bureau.)

A.850,000 B.85,000 C.650,000 D.44,000

* =