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  • A man rows a boat upstream a distance of 24 km and downstream the same distance in 6 hours. If the speed of the stream is 4 km/h, what is the speed of the man in still water?<div clas

A man rows a boat upstream a distance of 24 km and downstream the same distance in 6 hours. If the speed of the stream is 4 km/h, what is the speed of the man in still water?

Option: 1

6 km/h


Option: 2

9 km/h


Option: 3

10 km/h

 


Option: 4

12 km/h


Answers (1)

best_answer

Let's denote the speed of the man in still water as "m" (in km/h).

When the man rows upstream, his speed relative to the water (i.e., the speed of the boat minus the speed of the stream) is (m - 4) km/h. So, the time it takes him to row upstream 24 km is:

\mathrm{time=\frac{distance}{speed}}

\mathrm{time=\frac{24}{m-4}}

When the man rows downstream, his speed relative to the water (i.e., the speed of the boat plus the speed of the stream) is (m + 4) km/h. So, the time it takes him to row downstream 24 km is:

\mathrm{time=\frac{distance}{speed}}

\mathrm{time=\frac{24}{m+4}}

According to the problem, these two times add up to 6 hours:

\mathrm{ \frac{24}{m-4}+\frac{24}{m+4}=6}

Multiplying both sides by (m - 4)(m + 4), we get:

\mathrm{24 (m+4) + 24 (m-4) = 6(m-4)(m+4)}

Simplifying this equation, we get:

\mathrm{ 48=6m^{2}-48}

Rearranging, we get a quadratic equation:

  \mathrm{6m^{2}-48m-48=0}

Dividing both sides by 6, we get:

\mathrm{m^{2}-8m-8=0}

We can solve this quadratic equation using the quadratic formula:

\mathrm{ m=\frac{(8\pm \sqrt{(-8^{2})-4\times 1\times (-8)}}{2\times 1}}

\mathrm{ m=\frac{(8\pm \sqrt{(96)}}{2}}

Since the speed of the man in still water cannot be negative, we take the positive root:

\mathrm{m= 4+2\sqrt{(6)}\approx 8.89 km/hr}

Therefore, the speed of a man in still water is approximately 9 km/h.

Posted by

shivangi.bhatnagar

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