Albert started driving from City R towards City S at 15 40 at an average speed of 60 km/h. Riordan began driving from City R towards City S at 17 30 at an average speed of 110 km/h.

1. At what time did Riordan pass Albert on the road?
2. 1¹₁₀ hours after passing Albert, Riordan reached City S. At what time did Albert reach City S?

(a)
From 15 40 to 17 30 = 1 h 50 min

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

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

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

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

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

2 h 12 min after 17 30 = 19 42

Time that Riordan passed Albert on the road = 19 42

(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 City R and City S
= 3³₁₀ x 110
= 363 km

Time that Albert travelled from City R to City S
= 363 ÷ 60
= 6.05 h
= 6 h 3 min

6 h 3 min after 15 40 = 21 43

Time that Albert reached City S = 21 43

Answer: (a) 19 42; (b) 21 43