Chapter 8 linear appliCaTionS 287

Let t represent the number of hours the second car has traveled after pass-

ing the intersection.

drt

t

t

t

=

=

=

=

10 5

10

5

2

It will take the second car 2 hours to overtake the first.

PRACTICE

1. Lori starts jogging from a certain point and runs 5 mph. Jeffrey jogs
   from the same point 15 minutes later at a rate of 8 mph. How long will
   it take Jeffrey to catch up to Lori?


2. A truck driving east at 50 mph passes a certain mile marker. A motorcy-
   clist also driving east passes that same mile marker 45 minutes later. If
   the motorcyclist is driving 65 mph, how long will it take for the motor-
   cyclist to pass the truck?

✔SOLUTIONS

1. Lori has jogged
   rt=d

(^5) ()^1560 =^54
miles before Jeffrey began. Jeffrey is catching up to Lori at the rate of
8 – 5 = 3 mph. How long will it take someone traveling 3 mph to cover
(^54) miles?
Let t represent the number of hours Jeffrey jogs.
3 5
4
1
3
5
4
5
12
t
t
t

=⋅

Jeffrey will catch up to Lori in 125 hours or () 125 () 60 = 25 minutes.
PRACTICE

1. Lori starts jogging from a certain point and runs 5 mph. Jeffrey jogs