quadratic equation
2012-06-19 4:13 am
Tom and Mary are due south and due east of a bus stop respectively,and the distance between them is 60m.They walk towards the bus stop at the same time with their own constant speeds.After 6 seconds,they are both 27 m away from the bus stop.If Mary walks slower than Tom by 2m/s,find their speeds.
回答 (2)
2012-06-19 6:54 am
✔ 最佳答案
Let b m/s be the speed of Tom, and g m/s be that of Mary.Mary walks slower than Tom by 2m/s :
b = g + 2 ...... [1]
By Pythagorean theorem :
(6b + 27)² + (6g + 27)² = 60² ...... [2]
Put [1] into [2] :
[6(g + 2) + 27]² + (6g + 27)² = 60²
(6g + 39)² + (6g + 27)² = 60²
36g² + 468g + 1521 + 36g² + 324g + 729 = 3600
72g² + 792g - 1350 = 0
4g² + 44g - 75 = 0
(2g - 3)(2g + 25) = 0
g = 1.5 or g = -25/2 (rejected)
Put g = 1.5 into [1] :
b = 1.5 + 2
b = 3.5
Hence, Tom's speed is 3.5 m/s, and Mary's speed is 1.5 m/s.
2012-06-18 22:58:17 補充：
To 知識貧民：
This is a quadratic equation, but NOT a linear equation.
36x² + 36x² is equal to 72x², but NOT 0.
參考: andrew
2012-06-19 5:11 am
Let x ms^-1 be the speed of Mary.
[6(x+2)+27]²+(6x+27)²=60² (pyth. thm.)
792x=1350
x=1.70 ms^-1
.·.Mary's speed is 1.70 ms^-1
Tom's speed is 1.70+2 = 3.70 ms^-1
ps. speed x time = distance
2012-06-19 05:27:11 補充：
I see. Thank you for correcting me.
2012-06-19 05:29:12 補充：
what a huge mistake = =
thanks
[6(x+2)+27]²+(6x+27)²=60² (pyth. thm.)
792x=1350
x=1.70 ms^-1
.·.Mary's speed is 1.70 ms^-1
Tom's speed is 1.70+2 = 3.70 ms^-1
ps. speed x time = distance
2012-06-19 05:27:11 補充：
I see. Thank you for correcting me.
2012-06-19 05:29:12 補充：
what a huge mistake = =
thanks
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https://hk.answers.yahoo.com/question/index?qid=20120618000051KK00561