City N and City P are 360 km apart. At 5.18 p.m., Zane is travelling at a uniform speed left City N for City P while Jack set off from City P to City N along the same road at a uniform speed, which was 6 km/h slower than that of Zane. The two met at 8.18 p.m.
- Find the speed of Zane.
- 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 Zane and Jack to travel from 5.18 p.m. to 8.18 p.m. = 3 h
Average speed of Zane and Jack
= 360 ÷ 3
= 120 km/h
Zane's speed
= (120 + 6) ÷ 2
= 126 ÷ 2
= 63 km/h
(b)
Jack's speed
= 63 - 6
= 57 km/h
Distance that Jack travelled in 3 h
= 3 x 57
= 171 km
Remaining distance that Jack needed to travel
= 360 - 171
= 189 km
Time that Jack needed to reach his destination after the two met
= 189 ÷ 57
= 3
1857 = 3
619 h
Answer(s): (a) 63 km/h; (b) 3
619 h