Lucy started jogging from the farm to the park at a speed of 100 m/min at 7 a.m. Her sister started jogging from the farm later. They were beside each other at 7.45 a.m. and her sister reached the park at 8 a.m. while Lucy was still 1200 m away. If both of them travelled at a constant speed throughout the journey, what time did her sister leave the farm?
1 h = 60 min

From 7 a.m. to 8 a.m. = 1 h
From 7.45 a.m. to 8 a.m. = 15 min

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

Distance that Lucy's sister had to cover to catch up with Lucy
= 45 x 100
= 4500 m

Distance that Lucy's sister travelled to the park after catching up with Lucy
= 7200 - 4500
= 2700 m

Since Lucy's sister jogged 2700 m in 45 min,
Lucy's sister average speed
= 2700 ÷ 15
= 180 m/min

Duration that Lucy's sister took to jog to the park
= 7200 ÷ 180
= 40 min

Time that Lucy's sister left the farm:
40 min before 8 a.m. = 7.20 a.m.

Answer(s): 7.20 a.m.