Question

Mr. Morales drove 360 to a conference. He had transmission problems on the return trip and it took him 3 hours longer at an average speed of 30 mph less than the trip going. What was his average speed on the return trip?

Answer 1

Remember that

The speed is equal to divide the distance by the time

speed=d/t

Let

t ----> time spend to go to the conference in hours

s ----> speed trip going

Conference trip

s=360/t ------> equation 1

Return trip

speed=360/(t+3)

speed=s-30

s-30=360/(t+3) ------> equation 2

substitute equation 1 in equation 2

(360/t)-30=360/(t+3)

Multiply both sides by t(t+3) to remove fractions

360(t+3)-30t(t+3)=360t

360t+1,080-30t^2-90t=360t

simplify

30t^2+90t-1,080=0

Solve the quadratic equation

The solutions for t are

t=-7.7 h -----> is not a solution, because is a negative number

t=4.69 hours

Find out the average speed on the return trip

speed=360/(t+3)

speed=360/(4.69+3)

speed=46.81 mph