City R and City S are 456 km apart. At 3.59 p.m., Daniel is travelling at a uniform speed left City R for City S while David set off from City S to City R along the same road at a uniform speed, which was 10 km/h slower than that of Daniel. The two met at 7.59 p.m.
- Find the speed of Daniel.
- If David 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 David to travel from 3.59 p.m. to 7.59 p.m. = 4 h
Average speed of Daniel and David
= 456 ÷ 4
= 114 km/h
Daniel's speed
= (114 + 10) ÷ 2
= 124 ÷ 2
= 62 km/h
(b)
David's speed
= 62 - 10
= 52 km/h
Distance that David travelled in 4 h
= 4 x 52
= 208 km
Remaining distance that David needed to travel
= 456 - 208
= 248 km
Time that David needed to reach his destination after the two met
= 248 ÷ 52
= 4
4052 = 4
1013 h
Answer(s): (a) 62 km/h; (b) 4
1013 h