maths f.4 問題

Let x be the days that John needs to do the job,

then x + 5 is the day that Maria takes.


From the given condition,

6[1/x + 1/(x + 5)] = 1 ← (Since they need 6 days to work together to do the job.)

6[(x + 5) + x]/x(x + 5) = 1
6[(x + 5) + x]/x(x + 5) = 1
12x + 30 = x2 + 5x
x2 – 7x – 30 = 0
(x - 10)(x + 3) = 0
x = 10 or -3 (rejected)



So, John takes 10 days to finish the job.


Maria takes 15 days to finish the job.

Let the time it takes Maria to do the job alone be x days and that of John be y days.

x = y+ 5

1/x + 1/y = 1/6
Then 用代入法就計到答案la~

Let m and j be the number of days maria and john takes to do the job alone respectively

since maria takes 5 days more to do a job than john,
equation 1: m=j+5

the proportion of job each of them can do in one day time is 1/m and 1/j respectively,
thus they finished 1/6 of the work each day together
therefore,
equation 2: 1/m+1/j=1/6