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👨🏻‍🏫 學術台數學

[匿名]

2013-10-24 5:31 am

1. When a positive fraction is reduced to the simplest form, the numerator is greater than the denominator by 3. If 10 is added to both the numerator and the
denominator, the fraction obtained is 3/4 of the original.Find the original fraction.

2. If the speed of a car increased by 15 km/h in a journey of 240 km, 80 minutes would have been saved.Find the original speed of the car.

更新1:

Question2 , how about the original speed of the car?

更新2:

Sorry ,I am mistake

回答 (2)

用戶4366

2013-10-24 7:23 am

✔ 最佳答案

1. Let x be the denominator, then numerator is x+3.
original number = (x+3)/x

add 10 is (x+3+10)/(x+10) = (x+13)/(x+10)
then added result is (3/4) of the original number (x+3)/x

(x+13)/(x+10) = (3/4)(x+3)/x

x² + 13x - 90 = 0
(x+18)(x-5) = 0
x = 5 or x= -18 (reject < 0)

Original fraction is 8/5
add 10 = 18/15 = 6/5
(3/4)(8/5) = 24/20 = 6/5

2. Let v be the speed

original time needed = 240/v (h) 時間 = 距離 / 速率
timed need after adding speed = 240/(v+15)

time difference = 80/60 (h)
= 240/v - 240/(v+15)

80/60 = (240)(1/v - 1/(v+15)

v² + 15v -2700 = 0

v = 45 or v = -60 ( reject < 0)

240/45 = 5.33 hour
240/(45+15) = 4 hour
5.33-4 = 1.33 hour
1.33X60=79.8 minutes

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[匿名]

2013-10-25 3:34 am

忘了一問, 在time difference 那裡, 為何不是80/60 = 240/(v+15) - 240/v ?

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收錄日期: 2021-04-27 20:34:42
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