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

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 Yen ran = 45 min
Duration that Penelope 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 Yen ran
= 2 x 2700
= 5400 m

Distance that Penelope ran
= 3 x 2340
= 7020 m

Distance that Yen and Penelope 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