Question

A cutter travels down a river from point A to point B in 3hours and back in 6 hours. How long would it take the same cutter to travel the distance AB downstream with its motor shut off?

Answer 1

Answer: t₃ = 12 hr

Explanation:

The equations of motion of the cutter from A to B and B to A are:

S = (v₁ + v₂)t₁ and S = (v₁ - v₂)t₂, 

where t₁ = 3 hr is the time it takes the cutter to travel downstream, t₂ = 6 hr is the time it takes the cutter to travel upstream, v₁ is the speed of the cutter relative to the water, v₂ is the speed of the current, and S is the distance between points A and B. The equation of motion of the cutter with its motor switched off is S = v₂t₃. Solving these equations for t₃, we obtain

t₃ = 2t₁t₂/(t₂ - t₁) = 12hr.