City D and City E are 414 km apart. At 1.19 p.m., Nick is travelling at a uniform speed left City D for City E while Neave set off from City E to City D along the same road at a uniform speed, which was 6 km/h slower than that of Nick. The two met at 4.19 p.m.
- Find the speed of Nick.
- If Neave 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 Neave to travel from 1.19 p.m. to 4.19 p.m. = 3 h
Average speed of Nick and Neave
= 414 ÷ 3
= 138 km/h
Nick's speed
= (138 + 6) ÷ 2
= 144 ÷ 2
= 72 km/h
(b)
Neave's speed
= 72 - 6
= 66 km/h
Distance that Neave travelled in 3 h
= 3 x 66
= 198 km
Remaining distance that Neave needed to travel
= 414 - 198
= 216 km
Time that Neave needed to reach his destination after the two met
= 216 ÷ 66
= 3
1866 = 3
311 h
Answer(s): (a) 72 km/h; (b) 3
311 h