Olivia started jogging from the boutique to the reservoir at a speed of 100 m/min at 5 a.m. Her sister started jogging from the boutique later. They were beside each other at 5.36 a.m. and her sister reached the reservoir at 6 a.m. while Olivia was still 1200 m away. If both of them travelled at a constant speed throughout the journey, what time did her sister leave the boutique?
1 h = 60 min

From 5 a.m. to 6 a.m. = 1 h
From 5.36 a.m. to 6 a.m. = 24 min

Distance between the boutique and the reservoir
= 60 x 100 + 1200
= 6000 + 1200
= 7200 m

Distance that Olivia's sister had to cover to catch up with Olivia
= 36 x 100
= 3600 m

Distance that Olivia's sister travelled to the reservoir after catching up with Olivia
= 7200 - 3600
= 3600 m

Since Olivia's sister jogged 3600 m in 36 min,
Olivia's sister average speed
= 3600 ÷ 24
= 150 m/min

Duration that Olivia's sister took to jog to the reservoir
= 7200 ÷ 150
= 48 min

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

Answer(s): 5.12 a.m.