Application with uniform motion

Question

Darren drives to school in rush hour traffic and averages 32 mph. He returns home in mid-afternoon when there is less traffic and averages 48 mph. What is the distance between his home and school if the total traveling time is 1 hr 15 min?

Answer 1

T = time driving to school and F = time driving home

T + F = 1.25

32T = 48F (since the distance traveled is the same in either direction

 

Divide by 16 and then by 2 to get T = 3F/2

Substitute in the first equation and clear fractions immediately

3F + 2F = 2.5

5F = .5 and then T = .75

You should now plug in these values and make sure they solve the problem as stated.