City X and City Y are 456 km apart. At 1.19 p.m., Dylan is travelling at a uniform speed left City X for City Y while Liam set off from City Y to City X along the same road at a uniform speed, which was 12 km/h slower than that of Dylan. The two met at 3.19 p.m.
- Find the speed of Dylan.
- If Liam 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 Dylan and Liam to travel from 1.19 p.m. to 3.19 p.m. = 2 h
Average speed of Dylan and Liam
= 456 ÷ 2
= 228 km/h
Dylan's speed
= (228 + 12) ÷ 2
= 240 ÷ 2
= 120 km/h
(b)
Liam's speed
= 120 - 12
= 108 km/h
Distance that Liam travelled in 2 h
= 2 x 108
= 216 km
Remaining distance that Liam needed to travel
= 456 - 216
= 240 km
Time that Liam needed to reach his destination after the two met
= 240 ÷ 108
= 2
24108 = 2
29 h
Answer(s): (a) 120 km/h; (b) 2
29 h