City X and City Y are 396 km apart. At 1.30 p.m., Carl is travelling at a uniform speed left City X for City Y while Tom set off from City Y to City X along the same road at a uniform speed, which was 6 km/h slower than that of Carl. The two met at 3.30 p.m.
- Find the speed of Carl.
- If Tom 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 Tom to travel from 1.30 p.m. to 3.30 p.m. = 2 h
Average speed of Carl and Tom
= 396 ÷ 2
= 198 km/h
Carl's speed
= (198 + 6) ÷ 2
= 204 ÷ 2
= 102 km/h
(b)
Tom's speed
= 102 - 6
= 96 km/h
Distance that Tom travelled in 2 h
= 2 x 96
= 192 km
Remaining distance that Tom needed to travel
= 396 - 192
= 204 km
Time that Tom needed to reach his destination after the two met
= 204 ÷ 96
= 2
1296 = 2
18 h
Answer(s): (a) 102 km/h; (b) 2
18 h