Question

A rectangular swimming pool measures 30 meters by 50 meters. Tope swims back and forth the complete length of the pool parallel to the long side of the pool. She swims at a constant speed of 50 meters per minute. Meanwhile, her sister Tomi walks clockwise along the edges of the pool at a constant positive speed in such a way that they meet every time Tope reaches her starting point at the shorter side of the pool. What is Tomi's slowest possible walking speed, in meters per minute?

Answer 1

Tomi's slowest possible walking speed is 80 meters per minute

Explanation:

Tope swims at a speed of 50 meters per minute

Distance back and forth the long side of the pool is 50+50 meters = 100 meters

Time required to complete one round (back and forth) is 100 / 50 = 2 minutes

Perimeter of the pool is 50+50+30+30 = 160 meters

To walk around the perimeter and meet Tope at the starting point, Tomi has to walk 160 meters in 2 minutes

Tomi’s speed = 160 meters / 2 minutes or 160 / 2 = 80 meters per minute

Tomi's slowest possible speed should be 80 meters per minute