City P and City Q are 414 km apart. At 4.54 p.m., Pierre is travelling at a uniform speed left City P for City Q while Archie set off from City Q to City P along the same road at a uniform speed, which was 9 km/h slower than that of Pierre. The two met at 6.54 p.m.
- Find the speed of Pierre.
- If Archie 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 Pierre and Archie to travel from 4.54 p.m. to 6.54 p.m. = 2 h
Average speed of Pierre and Archie
= 414 ÷ 2
= 207 km/h
Pierre's speed
= (207 + 9) ÷ 2
= 216 ÷ 2
= 108 km/h
(b)
Archie's speed
= 108 - 9
= 99 km/h
Distance that Archie travelled in 2 h
= 2 x 99
= 198 km
Remaining distance that Archie needed to travel
= 414 - 198
= 216 km
Time that Archie needed to reach his destination after the two met
= 216 ÷ 99
= 2
1899 = 2
211 h
Answer(s): (a) 108 km/h; (b) 2
211 h