City B and City C are 560 km apart. At 1.38 p.m., Carl is travelling at a uniform speed left City B for City C while Reggie set off from City C to City B along the same road at a uniform speed, which was 12 km/h slower than that of Carl. The two met at 5.38 p.m.
- Find the speed of Carl.
- 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 Carl and Reggie to travel from 1.38 p.m. to 5.38 p.m. = 4 h
Average speed of Carl and Reggie
= 560 ÷ 4
= 140 km/h
Carl's speed
= (140 + 12) ÷ 2
= 152 ÷ 2
= 76 km/h
(b)
Reggie's speed
= 76 - 12
= 64 km/h
Distance that Reggie travelled in 4 h
= 4 x 64
= 256 km
Remaining distance that Reggie needed to travel
= 560 - 256
= 304 km
Time that Reggie needed to reach his destination after the two met
= 304 ÷ 64
= 4
4864 = 4
34 h
Answer(s): (a) 76 km/h; (b) 4
34 h