At 7 a.m., Vanessa and Lucy raced off together from the starting point of a path. Vanessa ran at an average speed of 2 m/s. Lucy ran at an average speed of 4 m/s. Upon reaching the end of the path, Lucy rested for 6 minutes. She then immediately ran back along the same route at 4 m/s. At 7.50 a.m., Vanessa met Lucy.

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 7 a.m. to 7.50 a.m. = 50 min

Duration that Vanessa ran = 50 min
Duration that Lucy ran = 50 -  6 = 44 min

1 min = 60 s

44 min = 44 x 60 = 2640 s
50 min = 50 x 60 = 3000 s

Distance that Vanessa ran
= 2 x 3000
= 6000 m

Distance that Lucy ran
= 4 x 2640
= 10560 m

Distance that Vanessa and Lucy ran
= 6000 + 10560
= 16560 m

1000 m = 1 km

16560 m = 16560 ÷ 1000 = 16.56 km

(b)
Length of the trail
= 16.56 ÷ 2
= 8.28 km

Answer(s): (a) 16.56 km; (b) 8.28 km