Irene started jogging from the library to the reservoir at a speed of 96 m/min at 9 a.m. Her cousin started jogging from the library later. They were beside each other at 9.45 a.m. and her cousin reached the reservoir at 10 a.m. while Irene 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 9 a.m. to 10 a.m. = 1 h
From 9.45 a.m. to 10 a.m. = 15 min

Distance between the library and the reservoir
= 60 x 96 + 1800
= 5760 + 1800
= 7560 m

Distance that Irene's cousin had to cover to catch up with Irene
= 45 x 96
= 4320 m

Distance that Irene's cousin travelled to the reservoir after catching up with Irene
= 7560 - 4320
= 3240 m

Since Irene's cousin jogged 3240 m in 45 min,
Irene's cousin average speed
= 3240 ÷ 15
= 216 m/min

Duration that Irene's cousin took to jog to the reservoir
= 7560 ÷ 216
= 35 min

Time that Irene's cousin left the library:
35 min before 10 a.m. = 9.25 a.m.

Answer(s): 9.25 a.m.