Question

A motorboat covers a certain distance downstream in a river in five hours. It covers
the same distance upstream in six hours. The speed of water is 2 km/h. Find the speed of the boat in still water.​

Answer 1

⛦ Given :

• Distance covered by motorboat downstream↓ in five hours.
• And it covers same distance upstream↑ in six hours.
• The speed of water is 2km/hr.

⛦ To find :

• The speed of the boat in still water.

⛦ Solution :

Let's assume the speed of the boat in still water as x km/h.

Speed of water(given) = 2km/h

•Speed of boat in downstream = (x+2) km/h

So, Distance covered in 5 hrs :

Speed × Time

= 5 × (x + 2) km = 5x + 10 km

•Speed of boat in upstream = (x - 2) km/h

So, Distance covered in 6 hrs :

Speed × Time

= 6 × (x - 2) km = 6x - 12 km

Now, As it is given that the boot covers the same distance upstream and downstream also.

Thus,

⟼ 6x - 12 = 5x + 10

⟼ 6x - 5x = 10 + 12

⟼ x = 22

∴ x = 22 km/h that is the speed of water in still water.

_________________

Checking the answer :

•Distance covered in 5 hours in downstream

= Speed × Time

= 5(x + 2) = 5(22 + 2)

= 110 + 10 = 120 km

•Distance covered in 6 hours in upstream

= Speed × Time

= 6(x - 2) = 6(22 - 2)

= 132 - 12 = 120 km.

Thus, in both the cases ,the distance is equal .Hence the Solution is correct.

Answer 2

Given:-

❍ Distance covered by motorboat downstream in five hours.

❍ The same distance upstream in six hours.

❍ Speed of water = 2km/hr.

To find:-

❍ Speed of the boat in still water.

Step by step explanation:-

❍ Let speed of motorboat = x km/h

$\implies$ Upstream distance = Downstream distance

$\longrightarrow$ 5 × (x + 2) km = 6 × (x - 2) km

$\longrightarrow$ 5x + 10 km = 6x - 2

$\longrightarrow$ x = 22 km/h

Hence,

x = 22 km/h is the speed of water in still water.

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