Amotorboat 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?

The speed of the current is 2 miles per hours

Step-by-step 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 =

So, x - y =

I.e  15 - y =  

And x + y =

I.e  15 + y =

=

I.e =

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 =  

∴   y = 2 miles per hour

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