City H and City J are 456 km apart. At 5.53 p.m., Xavier is travelling at a uniform speed left City H for City J while Cole set off from City J to City H along the same road at a uniform speed, which was 12 km/h slower than that of Xavier. The two met at 7.53 p.m.
- Find the speed of Xavier.
- If Cole 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 Xavier and Cole to travel from 5.53 p.m. to 7.53 p.m. = 2 h
Average speed of Xavier and Cole
= 456 ÷ 2
= 228 km/h
Xavier's speed
= (228 + 12) ÷ 2
= 240 ÷ 2
= 120 km/h
(b)
Cole's speed
= 120 - 12
= 108 km/h
Distance that Cole travelled in 2 h
= 2 x 108
= 216 km
Remaining distance that Cole needed to travel
= 456 - 216
= 240 km
Time that Cole 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