At 9 a.m., Hilda and Jean raced off together from the starting point of a path. Hilda ran at an average speed of 2 m/s. Jean ran at an average speed of 3 m/s. Upon reaching the end of the path, Jean rested for 5 minutes. She then immediately ran back along the same route at 3 m/s. At 9.45 a.m., Hilda met Jean.

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 9 a.m. to 9.45 a.m. = 45 min

Duration that Hilda ran = 45 min
Duration that Jean ran = 45 -  5 = 40 min

1 min = 60 s

40 min = 40 x 60 = 2400 s
45 min = 45 x 60 = 2700 s

Distance that Hilda ran
= 2 x 2700
= 5400 m

Distance that Jean ran
= 3 x 2400
= 7200 m

Distance that Hilda and Jean ran
= 5400 + 7200
= 12600 m

1000 m = 1 km

12600 m = 12600 ÷ 1000 = 12.6 km

(b)
Length of the trail
= 12.6 ÷ 2
= 6.3 km

Answer(s): (a) 12.6 km; (b) 6.3 km