Question

A motor boat goes downstream and covers a distance in 4 hours while it covers the same distance upstream in 5 hours.if the speed of the stream is 3 km/hr,find the speed of the motor boat in still water​

Answer 1

Explanation:

Let the speed of the motorboat be X.

speed of motorboat in downstream=x+3

speed of motorboat in downstream=x-3

since,distance=time x speed

therefore,

distance travelled by speed of X+3=4(X+3)

distance travelled by speed of x+-3=5(x-3)

since distance travelled was same, so

4(X+3)=5(x-3)

4x+12=5x-15

4x-5x=-15-12

-x=-27

X=27

Answer 2

Given:

✰ Time taken by a motor boat downstream = 4 hours

✰ Time taken by a motor boat upstream = 5 hours

✰ The speed of the stream = 3 km/hr

To find:

✠ The speed of the motor boat in still water ( S )

Solution:

Let the distance that the motor boat covers be 'x' km.

And the speed of motor boat in still water be 'S' km/h

• First we will find distance covered by a motor boat both downstream and upstream, then we will get two equations. Making both equations equal to one another, we will find 'S' that is the speed of the motor boat in still water.

According to the question,

♦ Speed of motor boat downstream = The speed of motor boat - The speed of the stream

♦ Speed of motor boat downstream = S + 3

♦ Speed of motor boat upstream = The speed of motor boat + The speed of the stream

♦ Speed of motor boat upstream = S - 3

In downstream,

❖ Distance = Speed × Time

• x = ( S + 3 )×4 ...①

In upstream,

❖ Distance = Speed × Time

• x = ( S - 3 )×5 ...②

From eq ① and ②

• ( S + 3 )×4 = ( S - 3 )×5

• 4S + 12 = 5S - 15

• 12 + 15 = 5S - 4S

• 27 = S

• S = 27 km/h

∴ The speed of the motor boat in still water ( S ) = 27 km/h

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