City H and City J are 360 km apart. At 3.45 p.m., Ivan is travelling at a uniform speed left City H for City J while Ian set off from City J to City H along the same road at a uniform speed, which was 6 km/h slower than that of Ivan. The two met at 6.45 p.m.
- Find the speed of Ivan.
- If Ian 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 Ian to travel from 3.45 p.m. to 6.45 p.m. = 3 h
Average speed of Ivan and Ian
= 360 ÷ 3
= 120 km/h
Ivan's speed
= (120 + 6) ÷ 2
= 126 ÷ 2
= 63 km/h
(b)
Ian's speed
= 63 - 6
= 57 km/h
Distance that Ian travelled in 3 h
= 3 x 57
= 171 km
Remaining distance that Ian needed to travel
= 360 - 171
= 189 km
Time that Ian needed to reach his destination after the two met
= 189 ÷ 57
= 3
1857 = 3
619 h
Answer(s): (a) 63 km/h; (b) 3
619 h