City T and City U are 360 km apart. At 5.16 p.m., Seth is travelling at a uniform speed left City T for City U while Luke set off from City U to City T along the same road at a uniform speed, which was 12 km/h slower than that of Seth. The two met at 8.16 p.m.
- Find the speed of Seth.
- If Luke 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 Seth and Luke to travel from 5.16 p.m. to 8.16 p.m. = 3 h
Average speed of Seth and Luke
= 360 ÷ 3
= 120 km/h
Seth's speed
= (120 + 12) ÷ 2
= 132 ÷ 2
= 66 km/h
(b)
Luke's speed
= 66 - 12
= 54 km/h
Distance that Luke travelled in 3 h
= 3 x 54
= 162 km
Remaining distance that Luke needed to travel
= 360 - 162
= 198 km
Time that Luke needed to reach his destination after the two met
= 198 ÷ 54
= 3
3654 = 3
23 h
Answer(s): (a) 66 km/h; (b) 3
23 h