Sam flew a distance of 500 miles at a normal speed. On the trip back Sam doubled the speed of the plane. How fast did Sam fly on the trip back if the total traveling time was 5 hours.

Question

I'm not really sure how to show the work for this problem

Answer 1

Sam flew a total distance of 1000 miles (500 there and 500 back) in a total a 5 hours. If speed was constant each way, then airspeed would be 200 mph.

But it is given that the return trip was at twice the speed as the first. This can be modelled as

500/s + 500/2s = 5.

Multiply 500/s by 2/2 to get 1000/2s + 500/2s = 5. This is done so that both fractions have the same denominator.

Add to get 1500/2s = 5

Multiply both sides by 2s to get 1500 = 10s

Divide both sides by 10 to get s = 150 mph (speed of outbound trip).

Therefore the trip back was at 2* 150 mph = 300 mph