Ray drives between towns A and B at an average speed of 75 km/h. Mahmoud drives the same distance at 80 km/h and takes 10 minutes less. What is the distance between A and B?

Answer 1

distance = rate of speed times time traveled

d = rt

Ray does the distance at 75 km/hr d= 75t

Muhammed does the distance d = 80(t-1/6) = 80t - 80/6 = 80t - 40/3 (10 minutes = 1/6 hour)

subtract to eliminate d to get

0 = 80t - 75t - 40/3

5t = 40/3

t = 8/3 = 2 2/3 hours

d = rt = 75(8/3) = 25(8) = 200 km

200 = 75 x 8/3 = 200 km

200 = 80 x (8/3 -1/6) = 80 x ( 15/6) = 80x5/2 = 200 km