City S and City T are 440 km apart. At 5.21 p.m., Luke is travelling at a uniform speed left City S for City T while Zane set off from City T to City S along the same road at a uniform speed, which was 10 km/h slower than that of Luke. The two met at 7.21 p.m.
- Find the speed of Luke.
- If Zane 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 Luke and Zane to travel from 5.21 p.m. to 7.21 p.m. = 2 h
Average speed of Luke and Zane
= 440 ÷ 2
= 220 km/h
Luke's speed
= (220 + 10) ÷ 2
= 230 ÷ 2
= 115 km/h
(b)
Zane's speed
= 115 - 10
= 105 km/h
Distance that Zane travelled in 2 h
= 2 x 105
= 210 km
Remaining distance that Zane needed to travel
= 440 - 210
= 230 km
Time that Zane needed to reach his destination after the two met
= 230 ÷ 105
= 2
20105 = 2
421 h
Answer(s): (a) 115 km/h; (b) 2
421 h