Solve the following word problem. a man travels from town x to town y at an average rate of 50 mph and returns at an average rate of 40 mph. he takes a 1/2 hour longer than he would take if he made the round trip at an average of 45 mph. what is the distance from town x to town y?

Distance = rate*time

Let distance from X to Y be 'd' 

From the equation we can solve for 'time'

time = distance/rate

The total time it takes to go 50 mph ,then 40 mph is:



The total time it takes to go 45 mph round trip is:



We know that the round-trip at 45 mph takes half-hour shorter, so by adding '1/2' to its time it will be equal to the time to go 50 then 40.



The distance from X to Y is 900 miles.