Suppose you hike up a hill at a rate of 4 mph You hike back

Suppose you hike up a hill at a rate of 4 mph. You hike back down the hill at 6 mph. The total time you spent on the hiking trip was 3 hours. How much time did it take you to hike up the hill?

Solution

Uphill DATA:
rate = 4 mph ; distance = x miles ; time = d/r = x/4 hrs.
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Downhill DATA:
rate = 6 mph ; distance = x miles ; time = x/6 hrs
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Equation:
time + time = 3 hrs
x/4 + x/6 = 3
3x + 2x = 36
5x = 36
x = 7.2 miles
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x/4 = 7.2/4 = 1.8 hrs (time to go up the hill)