Usha started jogging from the library to the nature reserve at a speed of 96 m/min at 6 a.m. Her sister started jogging from the library later. They were beside each other at 6.35 a.m. and her sister reached the nature reserve at 7 a.m. while Usha was still 1800 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 6.35 a.m. to 7 a.m. = 25 min

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

Distance that Usha's sister had to cover to catch up with Usha
= 35 x 96
= 3360 m

Distance that Usha's sister travelled to the nature reserve after catching up with Usha
= 7560 - 3360
= 4200 m

Since Usha's sister jogged 4200 m in 35 min,
Usha's sister average speed
= 4200 ÷ 25
= 168 m/min

Duration that Usha's sister took to jog to the nature reserve
= 7560 ÷ 168
= 45 min

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

Answer(s): 6.15 a.m.