Question

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?

Answer 1

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