City D and City E are 405 km apart. At 4.30 p.m., Luis is travelling at a uniform speed left City D for City E while Ivan set off from City E to City D along the same road at a uniform speed, which was 9 km/h slower than that of Luis. The two met at 7.30 p.m.
- Find the speed of Luis.
- If Ivan 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 Ivan to travel from 4.30 p.m. to 7.30 p.m. = 3 h
Average speed of Luis and Ivan
= 405 ÷ 3
= 135 km/h
Luis's speed
= (135 + 9) ÷ 2
= 144 ÷ 2
= 72 km/h
(b)
Ivan's speed
= 72 - 9
= 63 km/h
Distance that Ivan travelled in 3 h
= 3 x 63
= 189 km
Remaining distance that Ivan needed to travel
= 405 - 189
= 216 km
Time that Ivan needed to reach his destination after the two met
= 216 ÷ 63
= 3
2763 = 3
37 h
Answer(s): (a) 72 km/h; (b) 3
37 h