City R and City S are 450 km apart. At 1.50 p.m., Fabian is travelling at a uniform speed left City R for City S while Gabriel set off from City S to City R along the same road at a uniform speed, which was 10 km/h slower than that of Fabian. The two met at 4.50 p.m.
- Find the speed of Fabian.
- If Gabriel 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 Fabian and Gabriel to travel from 1.50 p.m. to 4.50 p.m. = 3 h
Average speed of Fabian and Gabriel
= 450 ÷ 3
= 150 km/h
Fabian's speed
= (150 + 10) ÷ 2
= 160 ÷ 2
= 80 km/h
(b)
Gabriel's speed
= 80 - 10
= 70 km/h
Distance that Gabriel travelled in 3 h
= 3 x 70
= 210 km
Remaining distance that Gabriel needed to travel
= 450 - 210
= 240 km
Time that Gabriel needed to reach his destination after the two met
= 240 ÷ 70
= 3
3070 = 3
37 h
Answer(s): (a) 80 km/h; (b) 3
37 h