[22 km/hr] The current of a stream runs at the rate of 2 km per hr. A motor boat goes 10 km upstream and back a

For Competitive Exams

The current of a stream runs at the rate of 2 km per hr. A motor boat goes 10 km upstream and back again to the starting point in 55 min. Find the speed of the motor boat in still water?

22 km/hr

12 km/hr

20 km/hr

16 km/hr

Explanation:

Let the speed of the boat in still water $=x$ km/hr

Speed of the current = 2 km/hr

Then, speed downstream $=\left(x+2\right)$ km/hr

speed upstream $=\left(x-2\right)$ km/hr

Total time taken to travel 10 km upstream and back = 55 minutes $=\dfrac{55}{60}$ hour = $\dfrac{11}{12}$ hour

$\Rightarrow \dfrac{10}{x-2} + \dfrac{10}{x+2} = \dfrac{11}{12}$

$120\left(x+2\right) + 120\left(x-2\right) = 11\left(x^2-4\right)$

$240x = 11x^2 - 44$

$11x^2 - 240x - 44 = 0$

$11x^2 - 242x +2x - 44 = 0$

$11x\left(x-22\right)+2\left(x-22\right)=0 $

$ \left(x-22\right)(11x+2)=0$

$x=22\text{ or }\dfrac{-2}{11}$

Since $x$ cannot be negative, $x$ = 22

i.e., speed of the boat in still water = 22 km/hr

Additional Questions

A boat covers a certain distance downstream in 4 hours but takes 6 hours to return upstream to the starting point. If the speed of the stream be 3 km/hr, find the speed of the boat in still water	Answer
A man can row three-quarters of a kilometre against the stream in 11$ \dfrac{1}{4} $ minutes and down the stream in 7$ \dfrac{1}{2} $ minutes. The speed in km/hr of the man in still water is:	Answer
The speed of a boat in still water is 8 kmph. If it can travel 1 km upstream in 1 hr, what time it would take to travel the same distance downstream?	Answer
A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?	Answer
In a river flowing at 2 km/hr, a boat travels 32 km upstream and then returns downstream to the starting point. If its speed in still water be 6 km/hr, find the total journey time.	Answer
A man can row 7.5 kmph in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of stream.	Answer
A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?	Answer
Tap A can fill the tank completely in 6 hrs while tap B can empty it by 12 hrs. By mistake, the person forgot to close the tap B, As a result, both the taps, remained open. After 4 hrs, the person realized the mistake and immediately closed the tap B. In how much time now onwards, would the tank be full?	Answer
A man rows to a place 48 km distant and come back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is:	Answer
The current of a stream runs at the rate of 2 km per hr. A motor boat goes 10 km upstream and back again to the starting point in 55 min. Find the speed of the motor boat in still water?	Answer

Share with Friends