The speed of a boat in still water is 10 mph If it travels o

The speed of a boat in still water is 10 mph. If it travels on a river 6 miles downstream in the same amount of time it takes to travel 3 miles upstream, what is the speed of the current?

Solution

let b = speed of the boat in still water.
let c = speed of the current
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rate * time = distance
let h = time
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going downstream, the formula is (b + c) * h = 6
going upstream, the formula is (b - c) * h = 3
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since b = 10, these formula become:
(10 + c) * h = 6
and
(10 - c) * h = 3
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since 6 = 2 * 3, then we can substitute (10 - c) * h for 3 to get:
(10 + c) * h = (10 - c) * h * 2
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this formula becomes:
10h + ch = 20h - 2ch
we add 2ch to both sides and we subtract 10h from both sides to get:
3ch = 10h
we divide both sides by h to get:
3c = 10
we divide both sides by 3 to get:
c = 10/3
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our first equation is:
(10 + c) * h = 6
we replace c with 10/3 to get:
(10 + 10/3) * h = 6
this becomes:
(40/3) * h = 6
we multiply both sides by 3 to get:
40 * h = 18
we divide both sides by 40 to get:
h = 18/40
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that\'s our answer.
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to prove the answer is correct, we substitute in the original formulas:
(10 + 10/3) * 18/40 = 6
this becomes:
(40/3) * 18/40 = 6
this becomes:
18/3 = 6 which becomes 6 = 6 which is true.
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(10 - 10/3) * 18/40 = 3
this becomes:
(20/3) * 18/40 = 3
this becomes:
(1/3) * (18/2) = 3
this becomes:
(1/3) * 9 = 3 which becomes 3 = 3 which is true3.
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answer checks out so h = 18/40 is good.