Usha started jogging from the hospital to the park at a speed of 105 m/min at 8 a.m. Her sister started jogging from the hospital later. They were beside each other at 8.45 a.m. and her sister reached the park at 9 a.m. while Usha was still 1800 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 8 a.m. to 9 a.m. = 1 h
From 8.45 a.m. to 9 a.m. = 15 min

Distance between the hospital and the park
= 60 x 105 + 1800
= 6300 + 1800
= 8100 m

Distance that Usha's sister had to cover to catch up with Usha
= 45 x 105
= 4725 m

Distance that Usha's sister travelled to the park after catching up with Usha
= 8100 - 4725
= 3375 m

Since Usha's sister jogged 3375 m in 45 min,
Usha's sister average speed
= 3375 ÷ 15
= 225 m/min

Duration that Usha's sister took to jog to the park
= 8100 ÷ 225
= 36 min

Time that Usha's sister left the hospital:
36 min before 9 a.m. = 8.24 a.m.

Answer(s): 8.24 a.m.