Question
Download Solution PDFA man rows a boat a certain distance downstream in 9 hours, while it takes 18 hours to row the same distance upstream. How many hours will it take him to row three-fifth of the same distance in still water?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A man rows a boat a certain distance downstream in 9 hours, while it takes 18 hours to row the same distance upstream.
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.
4. Componendo-Dividendo Method
Calculation:
Let the distance, speed of the boat in still water, and speed of the river be D, S, and R respectively.
According to the concept,
D/(S - R) = 18 ....(1)
D/(S + R) = 9 ....(2)
(1) ÷ (2),
(S + R)/(S - R) = 2
⇒ \(\frac {S + R + S - R}{S + R - S + R} = \frac {2 + 1} {2 - 1}\) (Componendo-Dividendo Method)
⇒ \(\frac {S}{R} = 3\)
⇒ S = 3R
Putting S = 3R in (1), D = 36R
Now, time taken to row three-fifth of the same distance in still water = \(36R \times \frac {3}{5} \div 3R\) = 7.2 hours
∴ It will take 7.2 hours to row three-fifth of the same distance in still water.
Shortcut Trick
Let's assume the total distance be 180 km
So, down-stream speed will be 180/9 = 20 km/hr
So, up-stream speed will be 180/18 = 10 km/hr
Now, speed of the boat will be (20 + 10)/2 = 15 km/hr
So,the boat can row (3/5th of 180km) 108 km in 108/15 = 7.2 hr
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