A man walked 12km at a constant speed, and then 6km further at a speed of 1/2 km/h faster. He would have saved 20 minutes if he completed the whole journey at the higher speed.
(a) What was his speed in the first 12km?
(b) If he walked in the speed obtained in (a) for the whold journey, how long would he take?
More about equation
2013-01-05 8:35 pm
回答 (2)
2013-01-06 1:30 am
✔ 最佳答案
(a) Let the speed be x km/hr.Time taken for the 1st 12km = 12/x hr.
Speed of the next 6km = (x + 1/2) km/hr.
Time take for this 6km = 6/(x + 1/2)
If whole journey is at (x + 1/2) km/hr., time require = (12 + 6)/(x + 1/2) hr.
So 12/x + 6/(x + 1/2) - 18/(x + 1/2) = 1/3
12/x - 12/(x + 1/2) = 1/3
12/x - 24/(2x + 1) = 1/3
36(2x + 1) - 72x = x(2x + 1)
72x + 36 - 72x = 2x^2 + x
2x^2 + x - 36 = 0
(2x + 9)(x - 4) = 0
x = - 9/2 (rej.) or 4 km/hr.
(b)
Time = (12 + 6)/4 = 18/4 = 4.5 hr.
2013-01-06 1:39 am
(a)Let x be his speed in the first 12km (unit: km/h)
Then x+0.5 is his speed in the next 6km
By the information given in the question, we may form the following equation
about time:
Time consumed in the journey with both low and high speed invloved=
Time consumed in the journey with only high speed involved+1/3
(Here low speed means x; high speed means x+0.5; 1/3 means the twenty
minutes saved)
12/x + 6/(x+0.5)=18/(x+0.5) +1/3
=> 18=x(x+0.5)
=> x=-4.5 or x=4
x=-4.5 is rejected since speed can't be negative
Therefore x=4km/h
(b)18/4=4.5h
Then x+0.5 is his speed in the next 6km
By the information given in the question, we may form the following equation
about time:
Time consumed in the journey with both low and high speed invloved=
Time consumed in the journey with only high speed involved+1/3
(Here low speed means x; high speed means x+0.5; 1/3 means the twenty
minutes saved)
12/x + 6/(x+0.5)=18/(x+0.5) +1/3
=> 18=x(x+0.5)
=> x=-4.5 or x=4
x=-4.5 is rejected since speed can't be negative
Therefore x=4km/h
(b)18/4=4.5h
參考: myself
收錄日期: 2021-04-25 22:40:18
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