Kylie started jogging from the library to the park at a speed of 100 m/min at 5 a.m. Her brother started jogging from the library later. They were beside each other at 5.40 a.m. and her brother reached the park at 6 a.m. while Kylie was still 1200 m away. If both of them travelled at a constant speed throughout the journey, what time did her brother leave the library?
1 h = 60 min

From 5 a.m. to 6 a.m. = 1 h
From 5.40 a.m. to 6 a.m. = 20 min

Distance between the library and the park
= 60 x 100 + 1200
= 6000 + 1200
= 7200 m

Distance that Kylie's brother had to cover to catch up with Kylie
= 40 x 100
= 4000 m

Distance that Kylie's brother travelled to the park after catching up with Kylie
= 7200 - 4000
= 3200 m

Since Kylie's brother jogged 3200 m in 40 min,
Kylie's brother average speed
= 3200 ÷ 20
= 160 m/min

Duration that Kylie's brother took to jog to the park
= 7200 ÷ 160
= 45 min

Time that Kylie's brother left the library:
45 min before 6 a.m. = 5.15 a.m.

Answer(s): 5.15 a.m.