City S and City T are 316 km apart. At 2.20 p.m., Mark is travelling at a uniform speed left City S for City T while Vaidev set off from City T to City S along the same road at a uniform speed, which was 6 km/h slower than that of Mark. The two met at 4.20 p.m.
- Find the speed of Mark.
- If Vaidev 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 Mark and Vaidev to travel from 2.20 p.m. to 4.20 p.m. = 2 h
Average speed of Mark and Vaidev
= 316 ÷ 2
= 158 km/h
Mark's speed
= (158 + 6) ÷ 2
= 164 ÷ 2
= 82 km/h
(b)
Vaidev's speed
= 82 - 6
= 76 km/h
Distance that Vaidev travelled in 2 h
= 2 x 76
= 152 km
Remaining distance that Vaidev needed to travel
= 316 - 152
= 164 km
Time that Vaidev needed to reach his destination after the two met
= 164 ÷ 76
= 2
1276 = 2
319 h
Answer(s): (a) 82 km/h; (b) 2
319 h