City D and City E are 500 km apart. At 6.35 p.m., Ahmad is travelling at a uniform speed left City D for City E while Vaidev set off from City E to City D along the same road at a uniform speed, which was 5 km/h slower than that of Ahmad. The two met at 10.35 p.m.

1. Find the speed of Ahmad.
2. If Vaidev 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 Ahmad and Vaidev to travel from 6.35 p.m. to 10.35 p.m. = 4 h

Average speed of Ahmad and Vaidev
= 500 ÷ 4
= 125 km/h

Ahmad's speed
= (125 + 5) ÷ 2
= 130 ÷ 2 
= 65 km/h

(b)
Vaidev's speed
= 65 - 5
= 60 km/h

Distance that Vaidev travelled in 4 h
= 4 x 60
= 240 km

Remaining distance that Vaidev needed to travel
= 500 - 240
= 260 km

Time that Vaidev needed to reach his destination after the two met
= 260 ÷ 60
= 4²⁰₆₀
= 4¹₃ h

Answer(s): (a) 65 km/h; (b) 4¹₃ h