A boat covers a certain distance against the stream in 9 hours 36 min and it covers the same distance along the stream in 6 hours. What is the ratio of the speed of the boat in still water to that of the stream?

Given:

A boat covers a certain distance against the stream in 9 hours 36 min and it covers the same distance along the stream in 6 hours.

Concept used:

1. Distance = Speed × Time

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

3. 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 the speed of the stream be S and R km/h respectively.

9 hours 36 minutes = 9 + 36/60 = 9.6 hours

Let the distance be D km.

Upstream speed = (S - R) km/h

Downstream speed = (S + R) km/h

​According to the question,

\(\frac {D}{S - R} = 9.6\)      ....(1)

\( \frac {D}{S + R} = 6\)     ....(2)

(1) ÷ (2),

\(\frac {S + R}{S - R} = \frac {9.6}{6}\)

⇒ 6S + 6R = 9.6S - 9.6R

⇒ 3.6S = 15.6R

⇒ S/R = 15.6/3.6

⇒ S : R  = 13 : 3

∴ The ratio of the speed of the boat in still water to that of the stream is 13 : 3.

 Alternate Method

We know, 9 hours 36 min = 576 min and 6 hour = 360 min

Through upstream (U) and downstream(D) distance is constant, then time ∝ 1/speed

Time ratio of U : D = 576 : 360 = 8 : 5, then Speed ratio of U : D = 5 : 8

Speed of boat = (D speed + U speed)/2 = (8 + 5)/2 = 13/2 

Speed of stream =  (D speed - U speed)/2 = (8 - 5)/2 = 3/2

So, Speed of boat : Speed of stream = 13/2 : 3/2 = 13 : 3