a boat has a speed of 15 mph in still water It travels downs

a boat has a speed of 15 mph in still water. It travels downstream from Greentown, in three-fifths of an hour. It then goes back upstream from Glenavon to Cambria, which is two miles downstream from Greentown, in three fithts of an hour. Find the rate of the current.

Solution

Let rate of the current be \"c\".
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Downstream DATA:
Time = (3/5) hr ; distance = x miles ; Rate = x/(3/5)= 5x/3 mph
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Upstream DATA:
Time = (3/5)hr ; distance= x-2 miles ; Rate = (x-2)/(3/5) = 5(x-2)/3 mph
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EQUATIONS:
Rate downstream: 15+c = 5x/3
Rate upstream : 15-c = 5(x-2)/3
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Add to get: 30 = [5x/3] + [5(x-2)/3]
Multiply thru by 3 to get:
5x + 5(x-2) = 90
10x=100
x = 10 miles
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Substitute into 15+c = 5x/3 to solve for \"c\":
15+c = 50/3
c = 50/3 - 45/3 = 5/3 mph
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Rate of the current is (5/3) mph