City R and City S are 330 km apart. At 1.42 p.m., Ben is travelling at a uniform speed left City R for City S while Peter set off from City S to City R along the same road at a uniform speed, which was 11 km/h slower than that of Ben. The two met at 3.42 p.m.
- Find the speed of Ben.
- If Peter 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 Ben and Peter to travel from 1.42 p.m. to 3.42 p.m. = 2 h
Average speed of Ben and Peter
= 330 ÷ 2
= 165 km/h
Ben's speed
= (165 + 11) ÷ 2
= 176 ÷ 2
= 88 km/h
(b)
Peter's speed
= 88 - 11
= 77 km/h
Distance that Peter travelled in 2 h
= 2 x 77
= 154 km
Remaining distance that Peter needed to travel
= 330 - 154
= 176 km
Time that Peter needed to reach his destination after the two met
= 176 ÷ 77
= 2
2277 = 2
27 h
Answer(s): (a) 88 km/h; (b) 2
27 h