City S and City T are 350 km apart. At 2.46 p.m., Michael is travelling at a uniform speed left City S for City T while Bobby set off from City T to City S along the same road at a uniform speed, which was 5 km/h slower than that of Michael. The two met at 4.46 p.m.
- Find the speed of Michael.
- 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 Michael and Bobby to travel from 2.46 p.m. to 4.46 p.m. = 2 h
Average speed of Michael and Bobby
= 350 ÷ 2
= 175 km/h
Michael's speed
= (175 + 5) ÷ 2
= 180 ÷ 2
= 90 km/h
(b)
Bobby's speed
= 90 - 5
= 85 km/h
Distance that Bobby travelled in 2 h
= 2 x 85
= 170 km
Remaining distance that Bobby needed to travel
= 350 - 170
= 180 km
Time that Bobby needed to reach his destination after the two met
= 180 ÷ 85
= 2
1085 = 2
217 h
Answer(s): (a) 90 km/h; (b) 2
217 h