City X and City Y are 306 km apart. At 4.48 p.m., Valen is travelling at a uniform speed left City X for City Y while Julian set off from City Y to City X along the same road at a uniform speed, which was 9 km/h slower than that of Valen. The two met at 6.48 p.m.
- Find the speed of Valen.
- If Julian 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 Valen and Julian to travel from 4.48 p.m. to 6.48 p.m. = 2 h
Average speed of Valen and Julian
= 306 ÷ 2
= 153 km/h
Valen's speed
= (153 + 9) ÷ 2
= 162 ÷ 2
= 81 km/h
(b)
Julian's speed
= 81 - 9
= 72 km/h
Distance that Julian travelled in 2 h
= 2 x 72
= 144 km
Remaining distance that Julian needed to travel
= 306 - 144
= 162 km
Time that Julian needed to reach his destination after the two met
= 162 ÷ 72
= 2
1872 = 2
14 h
Answer(s): (a) 81 km/h; (b) 2
14 h