members of a hiking club hiked to an overnight campsite at t

members of a hiking club hiked to an overnight campsite at the rate of 3 mph. The following morning they returned on horseback over the same route at 10 mph. The total time spent in going and returning was 6 1/2 hrs. find the distance to the campsite.
I know d= r x t, but don\'t know what to use for rate. 3 mph or 10 mph?

Solution

Hiking DATA:
rate = 3 mph ; distance = x miles ; time = d/r = x/3 hrs
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Riding DATA:
rate = 10 mph ; distance = x miles ; time = x/10 hrs
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Equation:
time + time = 13/2 hrs
x/3 + x/10 = 13/2
Multiply thru by 30 to get:
10x + 3x = 15*13
13x = 15*13
x = 15 miles (distance to the campsite)