How long does it take for a boat to travel 150 km up the river if it takes 2 hours to cover the same

How long does it take for a boat to travel 150 km up the river if it takes 2 hours to cover the same distance down the river? The speed of the boat in still water is 62.5 km / h.

S = 150 km.

t1 = 2 h.

V = 62.5 km / h.

t2 -?

Since the water in the river moves at a certain speed Vt, the speed of the boat relative to the shore when moving down the river V1 will be the sum of the boat’s own speed V and the river current speed Vt: V1 = V + Vt.

The time of movement of the boat behind the current t1 is expressed by the formula: t1 = S / V1 = S / (V + Vt).

V + Vt = S / t1.

VT = S / t1 – V.

VT = 150 km / 2 h – 62.5 km / h = 12.5 km / h.

The speed of the boat relative to the bank when moving up the river V2 will be the difference between the boat’s own speed V and the speed of the river flow Vt: V2 = V – Vt.

The time of movement of the boat against the current t2 is expressed by the formula: t2 = S / V2 = S / (V – Vt).

t2 = 150 km / (62.5 km / h – 12.5 km / h) = 3 h.

Answer: the boat will go up the river in time t2 = 3 hours.