City H and City J are 390 km apart. At 5.36 p.m., John is travelling at a uniform speed left City H for City J while Jack set off from City J to City H along the same road at a uniform speed, which was 10 km/h slower than that of John. The two met at 8.36 p.m.
- Find the speed of John.
- If Jack 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 John and Jack to travel from 5.36 p.m. to 8.36 p.m. = 3 h
Average speed of John and Jack
= 390 ÷ 3
= 130 km/h
John's speed
= (130 + 10) ÷ 2
= 140 ÷ 2
= 70 km/h
(b)
Jack's speed
= 70 - 10
= 60 km/h
Distance that Jack travelled in 3 h
= 3 x 60
= 180 km
Remaining distance that Jack needed to travel
= 390 - 180
= 210 km
Time that Jack needed to reach his destination after the two met
= 210 ÷ 60
= 3
3060 = 3
12 h
Answer(s): (a) 70 km/h; (b) 3
12 h