City K and City L are 462 km apart. At 6.51 p.m., Rael is travelling at a uniform speed left City K for City L while Valen 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 Rael. The two met at 9.51 p.m.
- Find the speed of Rael.
- If Valen 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 Valen to travel from 6.51 p.m. to 9.51 p.m. = 3 h
Average speed of Rael and Valen
= 462 ÷ 3
= 154 km/h
Rael's speed
= (154 + 10) ÷ 2
= 164 ÷ 2
= 82 km/h
(b)
Valen's speed
= 82 - 10
= 72 km/h
Distance that Valen travelled in 3 h
= 3 x 72
= 216 km
Remaining distance that Valen needed to travel
= 462 - 216
= 246 km
Time that Valen needed to reach his destination after the two met
= 246 ÷ 72
= 3
3072 = 3
512 h
Answer(s): (a) 82 km/h; (b) 3
512 h