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A motorboat can maintain a constant speed of 15 miles per hour relative to the water. The boat makes trip upstream to a certain point in 51 minutes; the return trip takes 39 minutes. What is the speed of the current?

1 Answer

4 votes

Answer:

The speed of the current is 2 miles per hours

Explanation:

Given as :

The speed of motorboat = x = 15 miles per hour

The time taken by motorboat trip upstream = 51 minutes

The time taken by motorboat trip downstream = 39 minutes

Let The speed of the current = y miles per hour

Let The total distance cover = A miles

So ,

Speed =
(\textrm Distance)/(\textrm Time)

So, x - y =
(A)/(51)

I.e 15 - y =
(A)/(51)

And x + y =
(A)/(39)

I.e 15 + y =
(A)/(39)


(x-y)/(x+y) =
(39)/(51)

I.e
(x-y)/(x+y) =
(13)/(17)

Or, 17 × (x - y) = 13 × (x + y)

Or, 17 x - 17 y = 13 x + 13 y

Or, 17 x - 13 x = 13 y + 17 y

Or, 4 x = 30 y

Now, ∵ x = 15 miles per hour

So, 4 × 15 = 30 y

Or, y =
(60)/(30)

∴ y = 2 miles per hour

Hence The speed of the current is 2 miles per hours Answer

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