At 9 a.m., Nicole and Diana raced off together from the starting point of a track. Nicole ran at an average speed of 3 m/s. Diana ran at an average speed of 4 m/s. Upon reaching the end of the track, Diana rested for 4 minutes. She then immediately ran back along the same route at 4 m/s. At 9.45 a.m., Nicole met Diana.

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 Nicole ran = 45 min
Duration that Diana 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 Nicole ran
= 3 x 2700
= 8100 m

Distance that Diana ran
= 4 x 2460
= 9840 m

Distance that Nicole and Diana ran
= 8100 + 9840
= 17940 m

1000 m = 1 km

17940 m = 17940 ÷ 1000 = 17.94 km

(b)
Length of the trail
= 17.94 ÷ 2
= 8.97 km

Answer(s): (a) 17.94 km; (b) 8.97 km