City E and City F are 336 km apart. At 3.54 p.m., Jack is travelling at a uniform speed left City E for City F while Fabian set off from City F to City E along the same road at a uniform speed, which was 8 km/h slower than that of Jack. The two met at 5.54 p.m.
- Find the speed of Jack.
- If Fabian 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 Jack and Fabian to travel from 3.54 p.m. to 5.54 p.m. = 2 h
Average speed of Jack and Fabian
= 336 ÷ 2
= 168 km/h
Jack's speed
= (168 + 8) ÷ 2
= 176 ÷ 2
= 88 km/h
(b)
Fabian's speed
= 88 - 8
= 80 km/h
Distance that Fabian travelled in 2 h
= 2 x 80
= 160 km
Remaining distance that Fabian needed to travel
= 336 - 160
= 176 km
Time that Fabian needed to reach his destination after the two met
= 176 ÷ 80
= 2
1680 = 2
15 h
Answer(s): (a) 88 km/h; (b) 2
15 h