The time taken by a boat to cover a certain distance downstream is 40% of the time taken by it to cover the same distance upstream. What is the ratio of the speed of the boat in still water to its speed going upstream?

Given:

The time taken by a boat to cover a certain distance downstream is 40% of the time taken by it to cover the same distance upstream.

Concept used:

Distance = Speed × Time

While rowing upstream, the upstream speed is the difference between the speed of the boat in still water and the speed of the flow.

While rowing downstream, the downstream speed is the addition of the speed of the boat in still water and the speed of the flow.

Calculation:

Let the speed of the boat in still water and steam be P and Q kmph respectively.

Upstream speed = (P - Q) kmph

Downstream speed = (P + Q) kmph

Let the distance be D.

According to the question,

\(\frac {D}{(P - Q)} \times 40\% = \frac {D}{(P + Q)} \)

⇒ \(\frac {1}{(P - Q)} \times \frac {2}{5} = \frac {1}{(P + Q)} \)

⇒ 2P + 2Q = 5P - 5Q

⇒ 3P = 7Q

⇒ \(\frac {P}{7} = \frac {Q}{3} = k (let)\)

So, P = 7k and Q = 3k

Upstream speed = 7k - 3k = 4k

Now, the ratio of the speed of the boat in still water to its speed going upstream = 7k : 4k

⇒ 7 : 4

∴ The ratio of the speed of the boat in still water to its speed going upstream is 7 : 4.