Question

a motorboat covers a given distance in 6 hrs moving downstream on a river. it covers the same distances in 10 hrs moving upstream the time it takes to cover the same distance in still water
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Answer 1

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Answer 2

Given,

A motorboat covers a given distance in 6 hrs moving downstream on a river.

It covers the same distances in 10 hrs moving upstream.

To find,

The time taken to cover the same distance in still water.

Solution,

We can simply solve this mathematical problem using the following process:

Let us assume that the speed of the boat in still water is x Km/hr and the speed of the stream is y km/hr.

Now, mathematically,

The net speed of the boat while traveling upstream

= (speed of the boat) - (speed of the stream)

= (x-y) Km/hr

And, the net speed of the boat while traveling downstream

= (speed of the boat) + (speed of the stream)

= (x+y) Km/hr

Mathematically,

Speed = distance covered/time taken

=> distance covered = (speed)×(time taken)

{Equation-1}

Now, according to the question;

The distance covered while traveling upstream = the distance covered while traveling downstream

=> (net speed of the boat while traveling upstream)×(time taken) = (net speed of the boat while traveling downstream)×(time taken)

{according to equation-1}

=> (x-y) Km/hr × 10 hours = (x+y) Km/hr × 6 hours

=>10x - 10y = 6x + 6y

=> 4x = 16y

=> x = 4y

=> (speed of the boat) = 4(speed of the stream)

{Equation-2}

Now, according to the question;

total distance covered while traveling downstream

= (net speed of the boat while traveling downstream)×(time taken)

= (x+y) Km/hr × 6 hours

= 6(x+y)

= 6(x+x/4)

= 6/4(5x)

= 15x/2

= 7.5x Km

Now, according to equation-1;

The time taken to cover the same distance in still water

= (total distance covered while traveling downstream)/(speed of the boat in still water)

= (7.5x Km)/(x Km/hr)

= 7.5 hours

Hence, the time taken to cover the same distance in still water is 7.5 hours.