City X and City Y are 516 km apart. At 4.51 p.m., Jack is travelling at a uniform speed left City X for City Y while Luke set off from City Y to City X along the same road at a uniform speed, which was 12 km/h slower than that of Jack. The two met at 7.51 p.m.
- Find the speed of Jack.
- 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 Jack and Luke to travel from 4.51 p.m. to 7.51 p.m. = 3 h
Average speed of Jack and Luke
= 516 ÷ 3
= 172 km/h
Jack's speed
= (172 + 12) ÷ 2
= 184 ÷ 2
= 92 km/h
(b)
Luke's speed
= 92 - 12
= 80 km/h
Distance that Luke travelled in 3 h
= 3 x 80
= 240 km
Remaining distance that Luke needed to travel
= 516 - 240
= 276 km
Time that Luke needed to reach his destination after the two met
= 276 ÷ 80
= 3
3680 = 3
920 h
Answer(s): (a) 92 km/h; (b) 3
920 h