SOLUTION: At 2:00 pm a runner heads north on a highway jogging at 10 mph. At 2:30 pm a driver heads north on the same highway to pick up the runner. If the car travels at 55 mph how long wil

Question 761298: At 2:00 pm a runner heads north on a highway jogging at 10 mph. At 2:30 pm a driver heads north on the same highway to pick up the runner. If the car travels at 55 mph how long will it take the driver to catch the runner?
Answer by ramkikk66(644) (Show Source): You can put this solution on YOUR website!
At 2:00 pm a runner heads north on a highway jogging at 10 mph. At 2:30 pm a driver heads north on the same highway to pick up the runner. If the car travels at 55 mph how long will it take the driver to catch the runner?
At 2:30 the distance between the car and the runner is 5 miles (since the runner covers 10 miles in a hour, or 5 miles in 30 minutes). The car has to cover this additional distance to catch the runner.
Let us say the car catches up after x min
In x min the runner would have run miles
in x min the car would have covered miles
The car has to cover whatever the runner has run in x min, plus the head start of 5 miles that the runner had.
So,
= +
Multiplying both sides by 60

Simplifying

Dividing both sides by 45

min

Car will catch up with the runner in 6.667 min

:)

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