Chapter 8 linear appliCaTionS 289

Katy left her house on bicycle heading north at 8 mph. At the same time,

her sister Molly headed south at 12 mph. How long will it take for them to

be 24 miles apart?

The distance between them is increasing at the rate of 8 + 12 = 20 mph. The

question then becomes “How long will it take someone moving 20 mph to

travel 24 miles?”

Let t represent the number of hours each girl is traveling.

20 24

24

20

6

5

(^115)
t
t
t

=

The girls will be 24 miles apart after 115 hours or 1 hour 12 minutes.
PRACTICE

1. Two airplanes leave an airport simultaneously—one heading east, the
   other west. The eastbound plane travels at 140 mph and the westbound
   plane travels at 160 mph. How long will it take for the planes to be
   750 miles apart?


2. Mary began walking home from school, heading south at a rate of
   4 mph. Sharon left school at the same time heading north at 6 mph.
   How long will it take for them to be 3 miles apart?


3. Two freight trains pass each other on parallel tracks. One train is travel-
   ing west, going 40 mph. The other is traveling east, going 60 mph. When
   will the trains be 325 miles apart?

✔SOLUTIONS

1. The planes are moving apart at a rate of 140 + 160 = 300 mph. Let
   t represent the number of hours the planes are flying.

300 750

750

300

(^212)
t
t
t

=

In 212 hours, or 2 hours 30 minutes, the planes will be 750 miles apart.
PRACTICE

1. Two airplanes leave an airport simultaneously—one heading east, the