Question 72

A boat takes 80 minutes to row 12 km upstream and 60 minutes to row 15 km downstream. How long will it take to row a distance of 36 km in still water?

Solution

Let's assume the speed of the boat in still water and the speed of the stream are B and C respectively.

Speed of boat downstream = (B+C)

Speed of boat upstream = (B-C)

A boat takes 80 minutes to row 12 km upstream and 60 minutes to row 15 km downstream.

$$\frac{12}{B-C}\ =\ \frac{80}{60}$$

$$\frac{12}{B-C}\ =\ \frac{4}{3}$$

$$\frac{3}{B-C}\ =\ \frac{1}{3}$$

(B-C) = 9    Eq.(i)

$$\frac{15}{B+C}\ =\ \frac{60}{60}$$

(B+C) = 15    Eq.(ii)

Add Eq.(i) and Eq.(ii).

(B-C)+(B+C) = 9+15

2B = 24

B = 12 km/h

Time taken by the boat to row a distance of 36 km in still water = $$\frac{36}{12}$$

= 3 hours

Video Solution

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