What is the distance from Town X to Town Y?

Question

A man travels from Town X to Town Y at an average rate of 60 mph and returns at an average rate of 50 mph. He takes a 1/2 hour longer than he would take if he made the round trip at an average of 55 mph

Answer 1

Let T6 = the time travelled at 60 mph and T5 = the time travelled at 50 mph.

Let D = the distance from town X to town Y

D/60 = T6 and D/50 = T5

(T5 + T6 -.5) * 55 = 2 * D

(D/50 + D/60 -.5)*55 = 2D

11D/10 + 11D/12 -27.5 = 2D

(66D + 55D -120D)/60 = 27.5

D/60=27.5

D=1650

 

You should verify that 1650 is correct by plugging it into the original equations!