At 10 a.m., Lucy and Zoe raced off together from the starting point of a route. Lucy ran at an average speed of 3 m/s. Zoe ran at an average speed of 4 m/s. Upon reaching the end of the route, Zoe rested for 5 minutes. She then immediately ran back along the same route at 4 m/s. At 10.45 a.m., Lucy met Zoe.

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 10 a.m. to 10.45 a.m. = 45 min

Duration that Lucy ran = 45 min
Duration that Zoe ran = 45 -  5 = 40 min

1 min = 60 s

40 min = 40 x 60 = 2400 s
45 min = 45 x 60 = 2700 s

Distance that Lucy ran
= 3 x 2700
= 8100 m

Distance that Zoe ran
= 4 x 2400
= 9600 m

Distance that Lucy and Zoe ran
= 8100 + 9600
= 17700 m

1000 m = 1 km

17700 m = 17700 ÷ 1000 = 17.7 km

(b)
Length of the trail
= 17.7 ÷ 2
= 8.85 km

Answer(s): (a) 17.7 km; (b) 8.85 km