City R and City S are 564 km apart. At 1.41 p.m., Pierre is travelling at a uniform speed left City R for City S while Sam set off from City S to City R along the same road at a uniform speed, which was 5 km/h slower than that of Pierre. The two met at 5.41 p.m.
- Find the speed of Pierre.
- If Sam 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 Sam to travel from 1.41 p.m. to 5.41 p.m. = 4 h
Average speed of Pierre and Sam
= 564 ÷ 4
= 141 km/h
Pierre's speed
= (141 + 5) ÷ 2
= 146 ÷ 2
= 73 km/h
(b)
Sam's speed
= 73 - 5
= 68 km/h
Distance that Sam travelled in 4 h
= 4 x 68
= 272 km
Remaining distance that Sam needed to travel
= 564 - 272
= 292 km
Time that Sam needed to reach his destination after the two met
= 292 ÷ 68
= 4
2068 = 4
517 h
Answer(s): (a) 73 km/h; (b) 4
517 h