Question

A boat goes 15 km upstream and 10 km downstream in
2
3 hours 15 minutes it goes 12 km upstream and 14 km
downstream in 3 hours. What is the speed of the boat in
still water?
​

Answer 1

Step-by-step explanation:

A boat goes 15 km upstream and 10.5 km downstream in 3 hours 15 minutes. It goes 12 km upstream and 14 km downstream in 3 hours. What is the speed of the boat in still water?

Let the speed of the boat in still water be x km/hour and let the speed of the current be y km/hour.

⇒ The net speed while going upstream is x−y km/hour and the net speed while going downstream is x+y km/hour.

⇒ The time taken for going 15 km upstream and 10.5 km downstream is

15x−y+10.5x+y=3.25, and,

The time taken for going 12 km upstream and 14 km downstream is

12x−y+14x+y=3.

Let 1x−y=m and 1x+y=n.

⇒15m+10.5n=3.25 and 12m+14n=3.

Solving these two simultaneous equations we get m=16 and n=114.

⇒x−y=1m=6 and x+y=1n=14.

Solving these two simultaneous equations we get x=10 and y=4.

⇒ The speed of the boat in still water is 10 km/hour.

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