At 11 a.m., Olivia and Emma raced off together from the starting point of a path. Olivia ran at an average speed of 2 m/s. Emma ran at an average speed of 3 m/s. Upon reaching the end of the path, Emma rested for 4 minutes. She then immediately ran back along the same route at 3 m/s. At 11.45 a.m., Olivia met Emma.

1. Find the total distance covered by the two runners when they met each other. Express your answer in km.
2. Find the length of the trail in km.

(a)
From 11 a.m. to 11.45 a.m. = 45 min

Duration that Olivia ran = 45 min
Duration that Emma ran = 45 -  4 = 41 min

1 min = 60 s

41 min = 41 x 60 = 2460 s
45 min = 45 x 60 = 2700 s

Distance that Olivia ran
= 2 x 2700
= 5400 m

Distance that Emma ran
= 3 x 2460
= 7380 m

Distance that Olivia and Emma ran
= 5400 + 7380
= 12780 m

1000 m = 1 km

12780 m = 12780 ÷ 1000 = 12.78 km

(b)
Length of the trail
= 12.78 ÷ 2
= 6.39 km

Answer(s): (a) 12.78 km; (b) 6.39 km