A train traveling between 2 towns arrives 9 minutes late whe

A train traveling between 2 towns arrives 9 minutes late when traveling at 36
mph. When it travels at 27 mph the train arrives 39 minutes late. How many
miles are there between the two towns?

Solution

Fast Rate DATA:
rate = 36 mph ; distance = x miles ; time = d/r = x/36 hrs
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Slow Rate DATA:
rate = 27 mph ; distance = x miles ; time = d/r = x/27 hrs
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Equation:
slow time - fast time = (1/2) hr
(x/27) - (x/36) = 1/2
(36x - 27x)/[27*36) = 1/2
9x = (27*36)/2
x = (27*2)
x = 54 miles
Distance between the towns is 54 miles.