Emma started jogging from the church to the park at a speed of 100 m/min at 5 a.m. Her sister started jogging from the church later. They were beside each other at 5.30 a.m. and her sister reached the park at 6 a.m. while Emma was still 1500 m away. If both of them travelled at a constant speed throughout the journey, what time did her sister leave the church?
1 h = 60 min

From 5 a.m. to 6 a.m. = 1 h
From 5.30 a.m. to 6 a.m. = 30 min

Distance between the church and the park
= 60 x 100 + 1500
= 6000 + 1500
= 7500 m

Distance that Emma's sister had to cover to catch up with Emma
= 30 x 100
= 3000 m

Distance that Emma's sister travelled to the park after catching up with Emma
= 7500 - 3000
= 4500 m

Since Emma's sister jogged 4500 m in 30 min,
Emma's sister average speed
= 4500 ÷ 30
= 150 m/min

Duration that Emma's sister took to jog to the park
= 7500 ÷ 150
= 50 min

Time that Emma's sister left the church:
50 min before 6 a.m. = 5.10 a.m.

Answer(s): 5.10 a.m.