City N and City P are 525 km apart. At 4.39 p.m., Vincent is travelling at a uniform speed left City N for City P while Elijah set off from City P to City N along the same road at a uniform speed, which was 7 km/h slower than that of Vincent. The two met at 7.39 p.m.
- Find the speed of Vincent.
- 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 Vincent and Elijah to travel from 4.39 p.m. to 7.39 p.m. = 3 h
Average speed of Vincent and Elijah
= 525 ÷ 3
= 175 km/h
Vincent's speed
= (175 + 7) ÷ 2
= 182 ÷ 2
= 91 km/h
(b)
Elijah's speed
= 91 - 7
= 84 km/h
Distance that Elijah travelled in 3 h
= 3 x 84
= 252 km
Remaining distance that Elijah needed to travel
= 525 - 252
= 273 km
Time that Elijah needed to reach his destination after the two met
= 273 ÷ 84
= 3
2184 = 3
14 h
Answer(s): (a) 91 km/h; (b) 3
14 h