Tammy started jogging from the library to the reservoir at a speed of 110 m/min at 5 a.m. Her cousin started jogging from the library later. They were beside each other at 5.42 a.m. and her cousin reached the reservoir at 6 a.m. while Tammy was still 1800 m away. If both of them travelled at a constant speed throughout the journey, what time did her cousin leave the library?
1 h = 60 min

From 5 a.m. to 6 a.m. = 1 h
From 5.42 a.m. to 6 a.m. = 18 min

Distance between the library and the reservoir
= 60 x 110 + 1800
= 6600 + 1800
= 8400 m

Distance that Tammy's cousin had to cover to catch up with Tammy
= 42 x 110
= 4620 m

Distance that Tammy's cousin travelled to the reservoir after catching up with Tammy
= 8400 - 4620
= 3780 m

Since Tammy's cousin jogged 3780 m in 42 min,
Tammy's cousin average speed
= 3780 ÷ 18
= 210 m/min

Duration that Tammy's cousin took to jog to the reservoir
= 8400 ÷ 210
= 40 min

Time that Tammy's cousin left the library:
40 min before 6 a.m. = 5.20 a.m.

Answer(s): 5.20 a.m.