Question

On a river, B is intermediate to and

equidistant from the two ends A and C. If a boat can go from A to B and back in 5 hours and 15 minutes and from A to C in 7 hours. Find the speed of the current if distance between A and C is 14 km.​

Answer 1

Solution :-

→ Time taken from A to C = 7 hours.

So,

→ Time taken from A to B = 3.5 hours. (Since B is intermediate.)

Also,

→ Time taken from A to B and B to A = 5+15min = 5(15/60) = 5(1/4) = (21/4) hours .

Therefore,

→ Time taken from B to A = (21/4) - 3.5 = (21/4) - (7/2) = (21 - 14)/4 = (7/4) hours .

Hence,

→ Time taken from C to A = (7/4) × 2 = 3.5 hours.

Now,

→ Distance between A to C = 14km.

→ usual Speed from A to C = D/T = 14/7 = 2 km/h .

→ usual speed from C to A = D/T = 14/3.5 = 4km/h.

Since 4 > 2.

Therefore,

→ Downstream speed = x + y = 4 km/h

→ upstream speed = x - y = 2km/h .

[ where x is speed of boat and y is speed of current .]

Hence,

→ Speed of current = (Downstream speed - upstream speed ) / 2

→ Speed of current = (4 - 2)/2 = 2/2 = 1 km/h .(Ans.)

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