City K and City L are 400 km apart. At 5.59 p.m., Valen is travelling at a uniform speed left City K for City L while Zane set off from City L to City K along the same road at a uniform speed, which was 8 km/h slower than that of Valen. The two met at 7.59 p.m.
- Find the speed of Valen.
- If Zane 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 Zane to travel from 5.59 p.m. to 7.59 p.m. = 2 h
Average speed of Valen and Zane
= 400 ÷ 2
= 200 km/h
Valen's speed
= (200 + 8) ÷ 2
= 208 ÷ 2
= 104 km/h
(b)
Zane's speed
= 104 - 8
= 96 km/h
Distance that Zane travelled in 2 h
= 2 x 96
= 192 km
Remaining distance that Zane needed to travel
= 400 - 192
= 208 km
Time that Zane needed to reach his destination after the two met
= 208 ÷ 96
= 2
1696 = 2
16 h
Answer(s): (a) 104 km/h; (b) 2
16 h