City L and City M are 420 km apart. At 5.45 p.m., Zeph is travelling at a uniform speed left City L for City M while Sam set off from City M to City L along the same road at a uniform speed, which was 10 km/h slower than that of Zeph. The two met at 8.45 p.m.

1. Find the speed of Zeph.
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 Zeph and Sam to travel from 5.45 p.m. to 8.45 p.m. = 3 h

Average speed of Zeph and Sam
= 420 ÷ 3
= 140 km/h

Zeph's speed
= (140 + 10) ÷ 2
= 150 ÷ 2 
= 75 km/h

(b)
Sam's speed
= 75 - 10
= 65 km/h

Distance that Sam travelled in 3 h
= 3 x 65
= 195 km

Remaining distance that Sam needed to travel
= 420 - 195
= 225 km

Time that Sam needed to reach his destination after the two met
= 225 ÷ 65
= 3³⁰₆₅
= 3⁶₁₃ h

Answer(s): (a) 75 km/h; (b) 3⁶₁₃ h