Olivia started jogging from the hospital to the nature reserve at a speed of 102 m/min at 8 a.m. Her sister started jogging from the hospital later. They were beside each other at 8.35 a.m. and her sister reached the nature reserve at 9 a.m. while Olivia was still 1700 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 8.35 a.m. to 9 a.m. = 25 min

Distance between the hospital and the nature reserve
= 60 x 102 + 1700
= 6120 + 1700
= 7820 m

Distance that Olivia's sister had to cover to catch up with Olivia
= 35 x 102
= 3570 m

Distance that Olivia's sister travelled to the nature reserve after catching up with Olivia
= 7820 - 3570
= 4250 m

Since Olivia's sister jogged 4250 m in 35 min,
Olivia's sister average speed
= 4250 ÷ 25
= 170 m/min

Duration that Olivia's sister took to jog to the nature reserve
= 7820 ÷ 170
= 46 min

Time that Olivia's sister left the hospital:
46 min before 9 a.m. = 8.14 a.m.

Answer(s): 8.14 a.m.