Question

Naomi rows a boat downstream for 231 miles. The return trip upstream took 12 hours longer. If the current flows at 2 mph, how fast does Naomi row in still water? She rows mph

Answer 1

Let in still water Naomi rows at x mph.

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Now as the current flows at 2 mph, so we have,

Speed in upstream = (x - 2) mph

Speed in downstream = (x + 2) mph

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Let Naomi rows for t hours while in downstream.

Then according to the given data, we have,

(x - 2)(t + 12) = 231...........(1)

And, (x + 2)t = 231.............(2)

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Now (1) - (2) gives,

(xt - 2t + 12x - 24) - (xt + 2t) = 0

i.e. 12x - 4t - 24 = 0

i.e. 4t = 12x - 24

i.e. t = 3x - 6

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So from (2), we have,

(x + 2)(3x - 6) = 231

i.e. 3x²​​​​​​ + 6x - 6x - 12 = 231

i.e. 3x²​​​​​​ = 231 + 12

i.e. 3x²​​​​​​ = 243

i.e. x²​​​​​​ = 243/3

i.e. x²​​​​​​ = 81

i.e. x²​​​​​​ = 9²

i.e. x = 9

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So Naomi rows at 9 mph