City X and City Y are 464 km apart. At 4.44 p.m., Xavier is travelling at a uniform speed left City X for City Y while Ivan set off from City Y to City X along the same road at a uniform speed, which was 8 km/h slower than that of Xavier. The two met at 6.44 p.m.
- Find the speed of Xavier.
- 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 Xavier and Ivan to travel from 4.44 p.m. to 6.44 p.m. = 2 h
Average speed of Xavier and Ivan
= 464 ÷ 2
= 232 km/h
Xavier's speed
= (232 + 8) ÷ 2
= 240 ÷ 2
= 120 km/h
(b)
Ivan's speed
= 120 - 8
= 112 km/h
Distance that Ivan travelled in 2 h
= 2 x 112
= 224 km
Remaining distance that Ivan needed to travel
= 464 - 224
= 240 km
Time that Ivan needed to reach his destination after the two met
= 240 ÷ 112
= 2
16112 = 2
17 h
Answer(s): (a) 120 km/h; (b) 2
17 h