City M and City N are 504 km apart. At 6.54 p.m., Japheth is travelling at a uniform speed left City M for City N while Vaidev set off from City N to City M along the same road at a uniform speed, which was 6 km/h slower than that of Japheth. The two met at 9.54 p.m.
- Find the speed of Japheth.
- 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 Japheth and Vaidev to travel from 6.54 p.m. to 9.54 p.m. = 3 h
Average speed of Japheth and Vaidev
= 504 ÷ 3
= 168 km/h
Japheth's speed
= (168 + 6) ÷ 2
= 174 ÷ 2
= 87 km/h
(b)
Vaidev's speed
= 87 - 6
= 81 km/h
Distance that Vaidev travelled in 3 h
= 3 x 81
= 243 km
Remaining distance that Vaidev needed to travel
= 504 - 243
= 261 km
Time that Vaidev needed to reach his destination after the two met
= 261 ÷ 81
= 3
1881 = 3
29 h
Answer(s): (a) 87 km/h; (b) 3
29 h