City X and City Y are 420 km apart. At 5.35 p.m., Daniel is travelling at a uniform speed left City X for City Y while Peter set off from City Y to City X along the same road at a uniform speed, which was 10 km/h slower than that of Daniel. The two met at 7.35 p.m.
- Find the speed of Daniel.
- 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 Daniel and Peter to travel from 5.35 p.m. to 7.35 p.m. = 2 h
Average speed of Daniel and Peter
= 420 ÷ 2
= 210 km/h
Daniel's speed
= (210 + 10) ÷ 2
= 220 ÷ 2
= 110 km/h
(b)
Peter's speed
= 110 - 10
= 100 km/h
Distance that Peter travelled in 2 h
= 2 x 100
= 200 km
Remaining distance that Peter needed to travel
= 420 - 200
= 220 km
Time that Peter needed to reach his destination after the two met
= 220 ÷ 100
= 2
20100 = 2
15 h
Answer(s): (a) 110 km/h; (b) 2
15 h