City C and City D are 414 km apart. At 5.29 p.m., Rael is travelling at a uniform speed left City C for City D while Vaidev set off from City D to City C along the same road at a uniform speed, which was 6 km/h slower than that of Rael. The two met at 8.29 p.m.
- Find the speed of Rael.
- 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 Rael and Vaidev to travel from 5.29 p.m. to 8.29 p.m. = 3 h
Average speed of Rael and Vaidev
= 414 ÷ 3
= 138 km/h
Rael's speed
= (138 + 6) ÷ 2
= 144 ÷ 2
= 72 km/h
(b)
Vaidev's speed
= 72 - 6
= 66 km/h
Distance that Vaidev travelled in 3 h
= 3 x 66
= 198 km
Remaining distance that Vaidev needed to travel
= 414 - 198
= 216 km
Time that Vaidev needed to reach his destination after the two met
= 216 ÷ 66
= 3
1866 = 3
311 h
Answer(s): (a) 72 km/h; (b) 3
311 h