City F and City G is 420 km apart. Fred left City F for City G at 10.00 a.m. travelling at an average speed of 70 km/h. Ethan left City F later than Fred and caught up with him at 1.00 p.m. Ethan was travelling at a speed of 72 km/h.

1. At what time did Ethan leave City F?
2. How much later did Fred arrive in City G than Ethan? Express your answer in h as a fraction or mixed number.

(a)
From 10.00 a.m. to 1.00 p.m. = 3 h

Distance that Fred covered when Ethan caught up with Fred
= 3 x 70
= 210 km

Time that Ethan took to travel 210 km
= 210 ÷ 72
= 2¹¹₁₂ h

1 h = 60 min
¹¹₁₂ h = ¹¹₁₂ x 60 = 55 min
2¹¹₁₂ h = 2 h 55 min

Time that Ethan left City F:
2 h 55 min before 1.00 p.m. = 10.05 a.m.

(b)
Remaining distance that they had to cover to reach City G
= 420 - 210
= 210 km

Duration that Ethan had to travel before reaching City G
= 210 ÷ 72
= 2¹¹₁₂ h

Duration that Fred had to travel before reaching City G
= 210 ÷ 70
= 3 h

Duration that Fred took to arrive later than Ethan in City G
= 3 - 2¹¹₁₂
= ¹₁₂ h

Answer(s): (a) 10.05 a.m.; (b) ¹₁₂ h