City A and City B are 596 km apart. At 6.43 p.m., Nick is travelling at a uniform speed left City A for City B while Fred set off from City B to City A along the same road at a uniform speed, which was 5 km/h slower than that of Nick. The two met at 10.43 p.m.
- Find the speed of Nick.
- 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 Nick and Fred to travel from 6.43 p.m. to 10.43 p.m. = 4 h
Average speed of Nick and Fred
= 596 ÷ 4
= 149 km/h
Nick's speed
= (149 + 5) ÷ 2
= 154 ÷ 2
= 77 km/h
(b)
Fred's speed
= 77 - 5
= 72 km/h
Distance that Fred travelled in 4 h
= 4 x 72
= 288 km
Remaining distance that Fred needed to travel
= 596 - 288
= 308 km
Time that Fred 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