At 11 a.m., Cathy and Barbara raced off together from the starting point of a pathway. Cathy ran at an average speed of 2 m/s. Barbara ran at an average speed of 3 m/s. Upon reaching the end of the pathway, Barbara rested for 6 minutes. She then immediately ran back along the same route at 3 m/s. At 11.45 a.m., Cathy met Barbara.

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 Cathy ran = 45 min
Duration that Barbara ran = 45 -  6 = 39 min

1 min = 60 s

39 min = 39 x 60 = 2340 s
45 min = 45 x 60 = 2700 s

Distance that Cathy ran
= 2 x 2700
= 5400 m

Distance that Barbara ran
= 3 x 2340
= 7020 m

Distance that Cathy and Barbara ran
= 5400 + 7020
= 12420 m

1000 m = 1 km

12420 m = 12420 ÷ 1000 = 12.42 km

(b)
Length of the trail
= 12.42 ÷ 2
= 6.21 km

Answer(s): (a) 12.42 km; (b) 6.21 km