City M and City N are 380 km apart. At 3.32 p.m., Luis is travelling at a uniform speed left City M for City N while Elijah set off from City N to City M along the same road at a uniform speed, which was 10 km/h slower than that of Luis. The two met at 5.32 p.m.
- Find the speed of Luis.
- If Elijah 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 Luis and Elijah to travel from 3.32 p.m. to 5.32 p.m. = 2 h
Average speed of Luis and Elijah
= 380 ÷ 2
= 190 km/h
Luis's speed
= (190 + 10) ÷ 2
= 200 ÷ 2
= 100 km/h
(b)
Elijah's speed
= 100 - 10
= 90 km/h
Distance that Elijah travelled in 2 h
= 2 x 90
= 180 km
Remaining distance that Elijah needed to travel
= 380 - 180
= 200 km
Time that Elijah needed to reach his destination after the two met
= 200 ÷ 90
= 2
2090 = 2
29 h
Answer(s): (a) 100 km/h; (b) 2
29 h