City B and City C are 534 km apart. At 6.22 p.m., Fabian is travelling at a uniform speed left City B for City C while Fred set off from City C to City B along the same road at a uniform speed, which was 10 km/h slower than that of Fabian. The two met at 9.22 p.m.
- Find the speed of Fabian.
- If Fred 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 Fred to travel from 6.22 p.m. to 9.22 p.m. = 3 h
Average speed of Fabian and Fred
= 534 ÷ 3
= 178 km/h
Fabian's speed
= (178 + 10) ÷ 2
= 188 ÷ 2
= 94 km/h
(b)
Fred's speed
= 94 - 10
= 84 km/h
Distance that Fred travelled in 3 h
= 3 x 84
= 252 km
Remaining distance that Fred needed to travel
= 534 - 252
= 282 km
Time that Fred needed to reach his destination after the two met
= 282 ÷ 84
= 3
3084 = 3
514 h
Answer(s): (a) 94 km/h; (b) 3
514 h