City J and City K are 414 km apart. At 4.58 p.m., Jenson is travelling at a uniform speed left City J for City K while Luke set off from City K to City J along the same road at a uniform speed, which was 12 km/h slower than that of Jenson. The two met at 7.58 p.m.
- Find the speed of Jenson.
- 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 Jenson and Luke to travel from 4.58 p.m. to 7.58 p.m. = 3 h
Average speed of Jenson and Luke
= 414 ÷ 3
= 138 km/h
Jenson's speed
= (138 + 12) ÷ 2
= 150 ÷ 2
= 75 km/h
(b)
Luke's speed
= 75 - 12
= 63 km/h
Distance that Luke travelled in 3 h
= 3 x 63
= 189 km
Remaining distance that Luke needed to travel
= 414 - 189
= 225 km
Time that Luke needed to reach his destination after the two met
= 225 ÷ 63
= 3
3663 = 3
47 h
Answer(s): (a) 75 km/h; (b) 3
47 h