City U and City V are 414 km apart. At 3.34 p.m., Xavier is travelling at a uniform speed left City U for City V while Mark set off from City V to City U along the same road at a uniform speed, which was 6 km/h slower than that of Xavier. The two met at 6.34 p.m.
- Find the speed of Xavier.
- If Mark 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 Mark to travel from 3.34 p.m. to 6.34 p.m. = 3 h
Average speed of Xavier and Mark
= 414 ÷ 3
= 138 km/h
Xavier's speed
= (138 + 6) ÷ 2
= 144 ÷ 2
= 72 km/h
(b)
Mark's speed
= 72 - 6
= 66 km/h
Distance that Mark travelled in 3 h
= 3 x 66
= 198 km
Remaining distance that Mark needed to travel
= 414 - 198
= 216 km
Time that Mark needed to reach his destination after the two met
= 216 ÷ 66
= 3
1866 = 3
311 h
Answer(s): (a) 72 km/h; (b) 3
311 h