City H and City J are 596 km apart. At 2.22 p.m., Fabian is travelling at a uniform speed left City H for City J while Sam set off from City J to City H along the same road at a uniform speed, which was 5 km/h slower than that of Fabian. The two met at 6.22 p.m.
- Find the speed of Fabian.
- If Sam 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 Sam to travel from 2.22 p.m. to 6.22 p.m. = 4 h
Average speed of Fabian and Sam
= 596 ÷ 4
= 149 km/h
Fabian's speed
= (149 + 5) ÷ 2
= 154 ÷ 2
= 77 km/h
(b)
Sam's speed
= 77 - 5
= 72 km/h
Distance that Sam travelled in 4 h
= 4 x 72
= 288 km
Remaining distance that Sam needed to travel
= 596 - 288
= 308 km
Time that Sam needed to reach his destination after the two met
= 308 ÷ 72
= 4
2072 = 4
518 h
Answer(s): (a) 77 km/h; (b) 4
518 h