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# a man averaged 50mph traveling from Denver to Minneapolis.

a man averaged 50mph traveling from Denver to Minneapolis. returning by a different route that covered the same amount of miles, he averaged 55mph. what is the distance between the two cities if his total time was 32hrs? i have no idea how to set up the equation to solve this problem. it is driving me crazy and is due Friday Apr19th. someone with math expertise please help!

Ray Atkinson :

This is the same D=RT formula. miles = (miles/hour) * hours
Trip one is D miles = 50 miles/hour * x hours
Trip two is D miles = 55 miles/hour * y hours
The miles are the same, and the total x+y=32, or y=32-x
50x = 55(32-x)
50x = 1760-55x
105x = 1760
x = 16.762 hours
y = 15.238 hours
x = 50*16.762 = 838.1 miles
y = 55*15.238 = 838.1 miles, so it checks both ways.