## Q 30/70 A motor boat covers a certain distance downstream in a river in 1 hours. It covers the same distance upstream in 5 hours.

Question

Q 30/70 A motor boat covers a certain distance
downstream in a river in 1 hours. It covers
the same distance upstream in 5 hours. The speed
of the water is 6.0 km/hr. The speed of the boat in
still water is:​

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3 weeks 2021-10-08T05:16:21+00:00 2 Answers 0 views 0

1. ## Given :–

• A motor boat covers a certain distance downstream in a river in 1 hours.
• It covers the same distance upstream in 5 hours.
• The speed of the water is 6.0 km/hr.

## To Find :-

• Speed of the boat in still water.

## Solution :-

Let,

The distance covered = s.

The speed of boat in still water = x km/hr.

We know that,

• Distance = Speed × Time

Given that,

• Time taken for downstream in a river = 1 hours.

Net speed of boat in downstream

= x + 6

=> s = (x + 6) × 1

=> s = x + 6 ……….(i)

Also given that,

The same distance upstream in 5 hours

= x – 6

=> s = (x – 6) × 5

=> s = 5x – 30 ………..(ii)

Form equation (i) and (ii),

s = (x – 6) = (5x – 30)

=> x + 6 = 5x – 30

=> x – 5x = -30 – 6

=> -4x = -36

=> x = -36/-4

=> x = 9 km/hr

• The speed of the boat in still water is 9 km/hr.
2. ### EXPLANATION.

A motor boat covers a certain distance

downstream in a river in 1 hours.

it coveres the same distance upstream in

5 hours .

The speed of the water is = 6 km/hr.

### Accordingtothequestion,

Let the distance covered = s

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

### => Distance = Speed X Time

Time taken for downstream = 1 hours.

Net speed of boat in downstream

=> ( x + 6 )

=> s = ( x + 6 ) X 1

=> s = ( x + 6 ) …..(1)

Time taken for upstream = 5 hours.

Net speed of boat in upstream.

=> ( x – 6 )

=> s = ( x – 6 ) X 5

=> s = (5x – 30) …….(2)

From equation (1) and (2) we get,

=> s = ( x + 6 ) = ( 5x – 30 )

=> x + 6 = 5x – 30

=> 6 + 30 = 5x – x

=> 36 = 4x

=> x = 9