Set up an equation and solve the following problem. Andy starts walking from point A at 2 miles per hour. One-half hour later, Aaron starts walking from point A at 4 miles per hour and follows the same route. How long (in hours) will it take Aaron to catch up with Andy?
A) 1 hour
B) 0.45 hour
C) 0.75 hour
D) 0.5 hour

Question

Quizplus · Accepted Answer

Let's call the time it takes Aaron to catch up with Andy "t" (in hours).

In that time, Andy has already been walking for 0.5 hours (since he started earlier). So he has covered a distance of:

distance = speed x time
distance = 2 x 0.5
distance = 1 mile

Now, we need to find out how long it takes Aaron to cover the same distance that Andy has already covered plus the distance that Andy has covered while Aaron was walking. So the distance that Aaron needs to cover is:

distance = 1 mile + Andy's distance

The time it takes Aaron to cover that distance is:

time = distance / speed
time = (1 + Andy's distance) / 4

But we know that Andy's distance is equal to his speed times the time he has been walking before Aaron starts, which is 0.5 hours. So we can substitute that in the equation:

time = (1 + 2 x 0.5) / 4
time = (1 + 1) / 4
time = 0.5 hours

So it will take Aaron 0.5 hours to catch up with Andy. Answer choice D is correct.

Set Up an Equation and Solve the Following Problem