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? ______ miles
Accepted Solution
A:
distance = rate*time
Let distance from X to Y be 'd'Β
From the equation we can solve for 'time'
time = distance/rate
The total time it takes to go 50 mph ,then 40 mph is:
[tex]\frac{d}{50} + \frac{d}{40}[/tex]
The total time it takes to go 45 mph round trip is:
[tex]\frac{2d}{45} [/tex]
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.