W.S 發問於 科學及數學數學 · 1 十年前

# maths f.4 問題

maria takes 5 days more to do a job than John. Together, they can do the job in 6 days.How long does it take each to do the job alone??

ans: Maria: 15 days John: 10 days,,

### 3 個解答

• 1 十年前
最愛解答

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.

資料來源： Myself~~~
• 1 十年前

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~

• 1 十年前

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