At 7 a.m., Diana and Opal raced off together from the starting point of a course. Diana ran at an average speed of 2 m/s. Opal ran at an average speed of 3 m/s. Upon reaching the end of the course, Opal rested for 5 minutes. She then immediately ran back along the same route at 3 m/s. At 7.45 a.m., Diana 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 7 a.m. to 7.45 a.m. = 45 min

Duration that Diana ran = 45 min
Duration that Opal 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 Diana ran
= 2 x 2700
= 5400 m

Distance that Opal ran
= 3 x 2400
= 7200 m

Distance that Diana and Opal ran
= 5400 + 7200
= 12600 m

1000 m = 1 km

12600 m = 12600 ÷ 1000 = 12.6 km

(b)
Length of the trail
= 12.6 ÷ 2
= 6.3 km

Answer(s): (a) 12.6 km; (b) 6.3 km