Question

A boat, which moves at 11 mph in water without a current, goes 117 miles upstream and 117 miles back again in 22 hours. Find the speed of the current to the nearest tenth

Answer 1

let b = speed of the boat in still water.
let c = speed of the current
rate * time = distance
let h = time
going downstream, the formula is (b + c) * h = 6
going upstream, the formula is (b - c) * h = 3
since b = 10, these formula become:
(10 + c) * h = 6
and
(10 - c) * h = 3

since 6 = 2 * 3, then we can substitute (10 - c) * h for 3 to get:
(10 + c) * h = (10 - c) * h * 2

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