Kathy started jogging from the hospital to the park at a speed of 115 m/min at 5 a.m. Her sister started jogging from the hospital later. They were beside each other at 5.35 a.m. and her sister reached the park at 6 a.m. while Kathy was still 1500 m away. If both of them travelled at a constant speed throughout the journey, what time did her sister leave the hospital?
1 h = 60 min

From 5 a.m. to 6 a.m. = 1 h
From 5.35 a.m. to 6 a.m. = 25 min

Distance between the hospital and the park
= 60 x 115 + 1500
= 6900 + 1500
= 8400 m

Distance that Kathy's sister had to cover to catch up with Kathy
= 35 x 115
= 4025 m

Distance that Kathy's sister travelled to the park after catching up with Kathy
= 8400 - 4025
= 4375 m

Since Kathy's sister jogged 4375 m in 35 min,
Kathy's sister average speed
= 4375 ÷ 25
= 175 m/min

Duration that Kathy's sister took to jog to the park
= 8400 ÷ 175
= 48 min

Time that Kathy's sister left the hospital:
48 min before 6 a.m. = 5.12 a.m.

Answer(s): 5.12 a.m.