Question

a mortor-boat whose speed is 30km/hr in water goes 30km downstream and comes back in a total time of 4hrs 30 minutes find the speed of the stream.

Answer 1

The speed of the stream is 22.36 km/h.

Explanation:

The course of the boat contains two stages of equal length. On the first one he is going downstream, so its resultant speed is "30 + x" km/h, where "x" is the speed of the stream. On the other hand for the second part of the course he is going against the stream, so the resultant speed is " 30 - x" km/h. The time of each course must be:

`t_1 = (30)/(30 + x)`

`t_2 = (30)/(30 - x)`

The sum of these times must be equal to the total time of the course, therefore:

`t_1 + t_2 = 4.5\\(30)/(30 + x) + (30)/(30 - x) = 4.5\\(30*(30 - x) + 30*(30 + x))/((30 + x)(30 - x)) = 4.5\\900 - 30*x + 900 + 30*x = 4.5*(900 - x^2)\\4050 - 4.5*x^2 = 1800\\4.5*x^2 = 4050 - 1800\\4.5*x^2 = 2250\\x^2 = (2250)/(4.5)\\x^2 = 500\\x = 22.36`

The speed of the stream is 22.36 km/h.