City R and City S are 561 km apart. At 6.44 p.m., Gabriel is travelling at a uniform speed left City R for City S while Xavier set off from City S to City R along the same road at a uniform speed, which was 11 km/h slower than that of Gabriel. The two met at 9.44 p.m.
- Find the speed of Gabriel.
- If Xavier 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 Gabriel and Xavier to travel from 6.44 p.m. to 9.44 p.m. = 3 h
Average speed of Gabriel and Xavier
= 561 ÷ 3
= 187 km/h
Gabriel's speed
= (187 + 11) ÷ 2
= 198 ÷ 2
= 99 km/h
(b)
Xavier's speed
= 99 - 11
= 88 km/h
Distance that Xavier travelled in 3 h
= 3 x 88
= 264 km
Remaining distance that Xavier needed to travel
= 561 - 264
= 297 km
Time that Xavier needed to reach his destination after the two met
= 297 ÷ 88
= 3
3388 = 3
38 h
Answer(s): (a) 99 km/h; (b) 3
38 h