288 algebra De mystif ieD
The truck traveled (^50) ()^4560 = ^752 miles. The motorcyclist is catching up
to the truck at a rate of 65 − 50 = 15 mph. How long will it take some-
body moving at a rate of 15 mph to cover^752 miles?
Let t represent the number of hours the motorcyclist has been driving
since passing the mile marker.
75
2
15
1
15
75
2
5
2
221
⋅=
=
t
t
t
t
The motorcyclist will overtake the truck in 212 hours.
When two bodies are moving in opposite directions, whether toward each
other or away from each other, the rate at which the distance between them is
changing, whether growing larger or smaller, is the sum of their individual rates.
EXAMPLE
Two cars meet at an intersection, one heading north; the other, south. If the
northbound driver drives at a rate of 30 mph and the southbound driver at
the rate of 40 mph, when will they be 35 miles apart?
The distance between them is growing at the rate of 30 + 40 = 70 mph. The
question then becomes, “how long will it take for someone moving 70 mph
to travel 35 miles?”
Let t represent the number of hours the cars travel after leaving the inter-
section.
70 35
35
70
1
2
t
t
t
=
In half an hour, the cars will be 35 miles apart.
EXAMPLE
Two cars meet at an intersection, one heading north; the other, south. If the