City H and City J are 480 km apart. At 1.56 p.m., Jack is travelling at a uniform speed left City H for City J while Bobby set off from City J to City H along the same road at a uniform speed, which was 10 km/h slower than that of Jack. The two met at 4.56 p.m.
- Find the speed of Jack.
- If Bobby 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 Jack and Bobby to travel from 1.56 p.m. to 4.56 p.m. = 3 h
Average speed of Jack and Bobby
= 480 ÷ 3
= 160 km/h
Jack's speed
= (160 + 10) ÷ 2
= 170 ÷ 2
= 85 km/h
(b)
Bobby's speed
= 85 - 10
= 75 km/h
Distance that Bobby travelled in 3 h
= 3 x 75
= 225 km
Remaining distance that Bobby needed to travel
= 480 - 225
= 255 km
Time that Bobby needed to reach his destination after the two met
= 255 ÷ 75
= 3
3075 = 3
25 h
Answer(s): (a) 85 km/h; (b) 3
25 h