Question

The speed of a motor boat in still water is 15km/hr. If it goes down the stream 30km and again return to the starting point in a total time of 4 hours and 30min. Find the speed of the stream

Answer 1

Answer:

The speed of the stream is 5 km/h .

Step-by-step explanation:

Given as :

The speed of motor boat in still water = x = 15 km/h

The distance cover in down stream = d = 30 km

Total time taken in going and back = t = 4 h + 30 min = 4.5 hours

Let The speed of the stream = y km/h

Speed of motor boat in down stream = ( x + y ) km/h

Speed of motor boat in up stream = ( x - y ) km/h

According to question

Time = $\dfrac{distance}{speed}$

Or, 4.5 = $\dfrac{30}{x + y}$ + $\dfrac{30}{x - y}$

Or, $\dfrac{4.5}{30}$ = $\dfrac{(x - y) + (x + y)}{(x+y) (x-y)}$

Or, 0.15 ( x² - y² ) = 2 x

Or,  0.15 ( 15² - y² ) = 2 × 15

Or, 225 - y² = $\dfrac{30}{0.15}$

Or, 225 - y² =200

∴ y² = 225 - 200

i.e y²  = 25

Or, y = √25 = 5 , - 5

So, The speed of the stream = y = 5 km/h

Hence, The speed of the stream is 5 km/h . Answer