form 5 maths
2012-09-14 6:59 am
peter drives his car for 18 minutes and mary drives her car for 15 minutes. it is known that both of them drive at uniform speeds and the total distance travelled by peter exceeds that of mary by 2 km. if at least one of their cars does not exceed 80km/h, find the max. possible distance that peter travels
回答 (1)
2012-09-14 8:35 am
✔ 最佳答案
Let p km/h be the speed of Peter, and m km/h be the speed of Mary.p(18/60) - m(15/60) = 2
18p - 15m = 120
6p - 5m = 40
6p = 5m + 40
p = (5m + 40)/6
Let D km be the distance that Peter travels.
When p ≤ 80 :
D = p(18/60) ≤ 80*(18/60)
D ≤ 24
When m ≤ 80 :
p ≤ (5*80 + 40)/6 = 220/3
Then, D = p(18/60) ≤ (220/3)*(18/60)
D ≤ 22
Since p ≤ 80 or m ≤ 80
thus D ≤ 24 or D≤ 22
The maximum possible distance that peter travels = 24 km/h
參考: micatkie
收錄日期: 2021-04-13 18:58:34
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