Luis started driving from Town W towards Town X at 14 45 at an average speed of 60 km/h. Riordan began driving from Town W towards Town X at 16 35 at an average speed of 110 km/h.

1. At what time did Riordan pass Luis on the road?
2. 1¹₁₀ hours after passing Luis, Riordan reached Town X. At what time did Luis reach Town X?

(a)
From 14 45 to 16 35 = 1 h 50 min

Time that Luis travelled before Riordan started driving = 1 h 50 min

1 h = 60 min
1 h 50 min = 1⁵⁰₆₀ h = 1⁵₆ h

Distance that Luis travelled before Riordan started driving
= 1⁵₆ x 60
= ¹¹₆ x 60
= 110 km

Difference between Riordan's and Luis's speed
= 110 - 60
= 50 km/h

Time that Riordan took to catch up with Luis
= 110 ÷ 50
= 2.2 h
= 2 h 12 min

2 h 12 min after 16 35 = 18 47

Time that Riordan passed Luis on the road = 18 47

(b)
1¹₁₀ h = 1 h 6 min

Total time that Riordan travelled
= 1 h 6 min + 2 h 12 min
= 3 h 18 min

3 h 18 min = 3¹⁸₆₀h = 3³₁₀h

Distance between Town W and Town X
= 3³₁₀ x 110
= 363 km

Time that Luis travelled from Town W to Town X
= 363 ÷ 60
= 6.05 h
= 6 h 3 min

6 h 3 min after 14 45 = 20 48

Time that Luis reached Town X = 20 48

Answer: (a) 18 47; (b) 20 48