City E and City F are 580 km apart. At 1.20 p.m., Vincent is travelling at a uniform speed left City E for City F while Ahmad set off from City F to City E along the same road at a uniform speed, which was 5 km/h slower than that of Vincent. The two met at 5.20 p.m.
- Find the speed of Vincent.
- If Ahmad 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 Vincent and Ahmad to travel from 1.20 p.m. to 5.20 p.m. = 4 h
Average speed of Vincent and Ahmad
= 580 ÷ 4
= 145 km/h
Vincent's speed
= (145 + 5) ÷ 2
= 150 ÷ 2
= 75 km/h
(b)
Ahmad's speed
= 75 - 5
= 70 km/h
Distance that Ahmad travelled in 4 h
= 4 x 70
= 280 km
Remaining distance that Ahmad needed to travel
= 580 - 280
= 300 km
Time that Ahmad needed to reach his destination after the two met
= 300 ÷ 70
= 4
2070 = 4
27 h
Answer(s): (a) 75 km/h; (b) 4
27 h