Question

It took a boat 2 hours to reach town A going upstream. The way back was 1h20 min. What is the speed of the boat in still water if the speed of the stream is 3 mph?

Answer 1

Given:

It took a boat 2 hours to reach town A going upstream.

The way back was 1h20 min.

If the speed of the stream is 3 mph

To find:

What is the speed of the boat in still water?

Solution:

Let's assume,

"d" → distance covered while going upstream or downstream

"u" → the speed of the boat in still water

"v" → the speed of the stream = 3 mph ... (given)

So,

Speed downstream = (u + v) mph = (u + 3) mph

Speed upstream = (u - v) mph = (u - 3) mph

We know the formula as:

$\boxed{\bold{Time = \frac{Distance}{Speed} }}$

Therefore,

The time taken while going upstream = $\frac{d}{u - v} = \frac{d}{u - 3}\:hr$

⇒ $2 = \frac{d}{u - 3}$ ..... (according to the question)

⇒ $d = 2(u - 3)$ ..... (i)

and

The time taken while going downstream = $\frac{d}{u + v} = \frac{d}{u + 3}\:hr$

⇒ $1\frac{20}{60} = \frac{d}{u + 3}$ ..... (according to the question)

⇒ $1\frac{1}{3} = \frac{d}{u + 3}$

⇒ $\frac{4}{3} = \frac{d}{u + 3}$

⇒ $d = \frac{4}{3} (u + 3)$ ..... (ii)

Since the distance covered is the same in both the cases, so from eq. (i)& (ii), we get

$2(u - 3) = \frac{4}{3} (u + 3)$

$\implies 2u - 6 = \frac{4}{3} u + 4$

$\implies 2u - 6 = \frac{4u + 12}{3}$

$\implies 3(2u - 6) = 4u + 12$

$\implies 6u - 18 = 4u + 12$

$\implies 6u - 4u = 18 + 12$

$\implies 2u = 30$

$\implies \bold{u = 30\:mph}$

Thus, the speed of the boat in still water is → 30 mph.

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