City M and City N are 510 km apart. At 2.51 p.m., Tommy is travelling at a uniform speed left City M for City N while Sam set off from City N to City M along the same road at a uniform speed, which was 10 km/h slower than that of Tommy. The two met at 5.51 p.m.

1. Find the speed of Tommy.
2. If Sam 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 Tommy and Sam to travel from 2.51 p.m. to 5.51 p.m. = 3 h

Average speed of Tommy and Sam
= 510 ÷ 3
= 170 km/h

Tommy's speed
= (170 + 10) ÷ 2
= 180 ÷ 2 
= 90 km/h

(b)
Sam's speed
= 90 - 10
= 80 km/h

Distance that Sam travelled in 3 h
= 3 x 80
= 240 km

Remaining distance that Sam needed to travel
= 510 - 240
= 270 km

Time that Sam needed to reach his destination after the two met
= 270 ÷ 80
= 3³⁰₈₀
= 3³₈ h

Answer(s): (a) 90 km/h; (b) 3³₈ h