City H and City J are 456 km apart. At 4.34 p.m., Ivan is travelling at a uniform speed left City H for City J while Vaidev set off from City J to City H along the same road at a uniform speed, which was 8 km/h slower than that of Ivan. The two met at 7.34 p.m.
- Find the speed of Ivan.
- 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 Ivan and Vaidev to travel from 4.34 p.m. to 7.34 p.m. = 3 h
Average speed of Ivan and Vaidev
= 456 ÷ 3
= 152 km/h
Ivan's speed
= (152 + 8) ÷ 2
= 160 ÷ 2
= 80 km/h
(b)
Vaidev's speed
= 80 - 8
= 72 km/h
Distance that Vaidev travelled in 3 h
= 3 x 72
= 216 km
Remaining distance that Vaidev needed to travel
= 456 - 216
= 240 km
Time that Vaidev needed to reach his destination after the two met
= 240 ÷ 72
= 3
2472 = 3
13 h
Answer(s): (a) 80 km/h; (b) 3
13 h