City R and City S are 486 km apart. At 5.35 p.m., Rael is travelling at a uniform speed left City R for City S while Tom set off from City S to City R along the same road at a uniform speed, which was 6 km/h slower than that of Rael. The two met at 8.35 p.m.
- Find the speed of Rael.
- If Tom 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 Tom to travel from 5.35 p.m. to 8.35 p.m. = 3 h
Average speed of Rael and Tom
= 486 ÷ 3
= 162 km/h
Rael's speed
= (162 + 6) ÷ 2
= 168 ÷ 2
= 84 km/h
(b)
Tom's speed
= 84 - 6
= 78 km/h
Distance that Tom travelled in 3 h
= 3 x 78
= 234 km
Remaining distance that Tom needed to travel
= 486 - 234
= 252 km
Time that Tom needed to reach his destination after the two met
= 252 ÷ 78
= 3
1878 = 3
313 h
Answer(s): (a) 84 km/h; (b) 3
313 h