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

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 Cathy ran = 45 min
Duration that Opal 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 Cathy ran
= 3 x 2700
= 8100 m

Distance that Opal ran
= 4 x 2460
= 9840 m

Distance that Cathy and Opal 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