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  • A boat travels downstream a certain distance in 4 hours and returns the same distance in 5 hours. If the speed of the boat in still water is 12 km/h, what is the speed of the stream? &nbs

A boat travels downstream a certain distance in 4 hours and returns the same distance in 5 hours. If the speed of the boat in still water is 12 km/h, what is the speed of the stream?

 

Option: 1

\mathrm{2km/h}


Option: 2

\mathrm{3km/h}


Option: 3

\mathrm{\frac{4}{3}km/h}


Option: 4

\mathrm{5km/h}


Answers (1)

best_answer

Let's assume that the distance between the two points is "d", and let "x" be the speed of the stream. We can use the following formula to solve the problem:

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

When the boat travels downstream, it gets a boost from the stream, so its effective speed is the sum of its speed in still water and the speed of the stream, i.e. 12 + x. When the boat travels upstream, it has to fight against the stream, so its effective speed is the difference between its speed in still water and the speed of the stream, i.e. 12 - x.

According to the problem statement, the boat travels downstream for 4 hours and upstream for 5 hours, covering the same distance both times. Using the formula above, we can write two equations:

\\d=(12+x) * 4 (\text{when traveling downstream})\\ \\d=(12-x) * 5 (\text{when traveling upstream})

We can simplify these equations :

\\4 (12 + x) = 5(12 - x)\\ \\48+4x=60-5x\\ \\9x=12\\ \\x=\frac{4}{3}

Therefore, the speed of the stream is \mathrm{\frac{4}{3}km/hr.}

Posted by

manish painkra

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