City E and City F are 408 km apart. At 5.48 p.m., Daniel is travelling at a uniform speed left City E for City F while Reggie set off from City F to City E along the same road at a uniform speed, which was 10 km/h slower than that of Daniel. The two met at 8.48 p.m.
- Find the speed of Daniel.
- If Reggie 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 Reggie to travel from 5.48 p.m. to 8.48 p.m. = 3 h
Average speed of Daniel and Reggie
= 408 ÷ 3
= 136 km/h
Daniel's speed
= (136 + 10) ÷ 2
= 146 ÷ 2
= 73 km/h
(b)
Reggie's speed
= 73 - 10
= 63 km/h
Distance that Reggie travelled in 3 h
= 3 x 63
= 189 km
Remaining distance that Reggie needed to travel
= 408 - 189
= 219 km
Time that Reggie needed to reach his destination after the two met
= 219 ÷ 63
= 3
3063 = 3
1021 h
Answer(s): (a) 73 km/h; (b) 3
1021 h