Two brothers work together to cut the grass in a garden in 2 hours. If the work separately, the younger brother requires 3 hours more than the elder brother to cut the grass. Suppose the elder brother takes x hours to cut the grass alone.
I done question (a) is...... Elder brother: Time to complete the job alone (hours)=x and Fraction of the job completed in 1 hour = 1/x. Younger brother: Time to complete the job alone (hours)=x+3 and Fraction of the job completed in 1 hour = 1/x+3
Question(b) How long does the elder brother take to cut the grass alone?
I don't know to set up an equation connecting the given quantities.
唔識做功課61
2015-04-11 5:57 am
回答 (2)
2015-04-11 6:06 am
✔ 最佳答案
In one hour, the elder brother will finish 1/x of the job.In one hour, the younger brother will finish 1/(x +3) of the job.
So in one hour, two together will finish 1/x + 1/(x + 3) of the job.
Since it takes them 2 hours to finish the job, so in 1 hour they can finish 1/2 of the job. That is
1/x + 1/(x + 3) = 1/2
2(x + 3) + 2x = x(x + 3)
2x + 6 + 2x = x^2 + 3x
x^2 - x - 6 = 0
(x - 3)(x + 2) = 0
x = 3 or - 2 (rej.)
So the elder brother can finish the job alone in 3 hours. The younger brother can finish the job alone in 6 hours.
2015-04-11 6:15 am
Oh i see......I forget to change the hours.Thank you for your help!
收錄日期: 2021-04-15 19:02:39
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