A motor boat traveling at 18 miles per hour traveled the len

A motor boat traveling at 18 miles per hour traveled the length of a lake in one-quarter of an hour less time than it took when traveling at 12 miles per hour. What was the length in miles of the lake?

Solution

Let the length of the lake be x miles.
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Fast-trip DATA:
rate = 18 mph ; distance = x miles ; time = x/18 hr.
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Slower-trip DATA:
rate = 12 mph ; distance = x miles ; time = x/12 hr.
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Equation:
slow time - fast time = 1/4 hr
x/12 - x/18 = 1/4
Multiply thru by 36 to get:
3x - 2x = 9
x = 9 miles