Fiona started jogging from the library to the nature reserve at a speed of 100 m/min at 6 a.m. Her sister started jogging from the library later. They were beside each other at 6.40 a.m. and her sister reached the nature reserve at 7 a.m. while Fiona was still 1200 m away. If both of them travelled at a constant speed throughout the journey, what time did her sister leave the library?
1 h = 60 min

From 6 a.m. to 7 a.m. = 1 h
From 6.40 a.m. to 7 a.m. = 20 min

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

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

Distance that Fiona's sister travelled to the nature reserve after catching up with Fiona
= 7200 - 4000
= 3200 m

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

Duration that Fiona's sister took to jog to the nature reserve
= 7200 ÷ 160
= 45 min

Time that Fiona's sister left the library:
45 min before 7 a.m. = 6.15 a.m.

Answer(s): 6.15 a.m.