City J and City K are 544 km apart. At 3.43 p.m., Nick is travelling at a uniform speed left City J for City K while Gabriel set off from City K to City J along the same road at a uniform speed, which was 8 km/h slower than that of Nick. The two met at 7.43 p.m.
- Find the speed of Nick.
- If Gabriel 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 Gabriel to travel from 3.43 p.m. to 7.43 p.m. = 4 h
Average speed of Nick and Gabriel
= 544 ÷ 4
= 136 km/h
Nick's speed
= (136 + 8) ÷ 2
= 144 ÷ 2
= 72 km/h
(b)
Gabriel's speed
= 72 - 8
= 64 km/h
Distance that Gabriel travelled in 4 h
= 4 x 64
= 256 km
Remaining distance that Gabriel needed to travel
= 544 - 256
= 288 km
Time that Gabriel needed to reach his destination after the two met
= 288 ÷ 64
= 4
3264 = 4
12 h
Answer(s): (a) 72 km/h; (b) 4
12 h