City L and City M are 324 km apart. At 4.52 p.m., Valen is travelling at a uniform speed left City L for City M while Sam set off from City M to City L along the same road at a uniform speed, which was 6 km/h slower than that of Valen. The two met at 6.52 p.m.
- Find the speed of Valen.
- If Sam 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 Sam to travel from 4.52 p.m. to 6.52 p.m. = 2 h
Average speed of Valen and Sam
= 324 ÷ 2
= 162 km/h
Valen's speed
= (162 + 6) ÷ 2
= 168 ÷ 2
= 84 km/h
(b)
Sam's speed
= 84 - 6
= 78 km/h
Distance that Sam travelled in 2 h
= 2 x 78
= 156 km
Remaining distance that Sam needed to travel
= 324 - 156
= 168 km
Time that Sam needed to reach his destination after the two met
= 168 ÷ 78
= 2
1278 = 2
213 h
Answer(s): (a) 84 km/h; (b) 2
213 h