Answer: t3 = 12 hr
Explanation:
The equations of motion of the cutter from A to B and B to A are:
- = (v1 + v2)t1 and * = (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 is the distance between points A and B. The equation of motion of the cutter with its motor switched * is = v2t3. Solving these equations for t3, we obtain
t3 = 2t1t2/(t2 - t1) = 12hr.
