Shannon started jogging from the museum to the reservoir at a speed of 100 m/min at 5 a.m. Her brother started jogging from the museum later. They were beside each other at 5.36 a.m. and her brother reached the reservoir at 6 a.m. while Shannon was still 1200 m away. If both of them travelled at a constant speed throughout the journey, what time did her brother leave the museum?
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 museum and the reservoir
= 60 x 100 + 1200
= 6000 + 1200
= 7200 m

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

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

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

Duration that Shannon's brother took to jog to the reservoir
= 7200 ÷ 150
= 48 min

Time that Shannon's brother left the museum:
48 min before 6 a.m. = 5.12 a.m.

Answer(s): 5.12 a.m.