City K and City L are 420 km apart. At 3.20 p.m., Tim is travelling at a uniform speed left City K for City L while Ben set off from City L to City K along the same road at a uniform speed, which was 10 km/h slower than that of Tim. The two met at 5.20 p.m.

1. Find the speed of Tim.
2. If Ben continued to travel at the same speed, how long would it take for him to reach his destination after the two met? Express your answer in mixed number.

(a)
Time taken for Tim and Ben to travel from 3.20 p.m. to 5.20 p.m. = 2 h

Average speed of Tim and Ben
= 420 ÷ 2
= 210 km/h

Tim's speed
= (210 + 10) ÷ 2
= 220 ÷ 2 
= 110 km/h

(b)
Ben's speed
= 110 - 10
= 100 km/h

Distance that Ben travelled in 2 h
= 2 x 100
= 200 km

Remaining distance that Ben needed to travel
= 420 - 200
= 220 km

Time that Ben needed to reach his destination after the two met
= 220 ÷ 100
= 2²⁰₁₀₀
= 2¹₅ h

Answer(s): (a) 110 km/h; (b) 2¹₅ h