Question

27) To do the same amount of work Raju takes 6 hours less time than Joseph. If both
together complete the same amount of work in 13 hours 20 minutes find how
much time Joseph will take to complete the work.​

Answer 1

Joseph will take 30 hrs to complete the work.

Step-by-step explanation:

It is given that Raju takes 6 hrs less than Joseph

So, if Joseph takes "x" hrs to do the work then Raju will take "(x - 6)" hrs to do the same amount of work.

Therefore,

The fraction of work done by Joseph in 1-day = $\frac{1}{x}$

The fraction of work done by Raju in 1-day = $\frac{1}{x-6}$

Also given that they together complete the same work in 13 hrs 20 minutes i.e., 13$\frac{20}{60}$ = 13$\frac{1}{3}$ = $\frac{40}{3}$ hrs

So, the fraction of work done by both Joseph and Raju = $\frac{3}{40}$

Therefore we can write the eq. as,

$\frac{1}{x} + \frac{1}{x - 6} = \frac{3}{40} \\ or, \frac{x - 6 + x}{x(x - 6)} = \frac{3}{40} \\ or, \frac{2x - 6}{x^2 - 6x} = \frac{3}{40}$

or, 40[2x - 6] = 3[x² - 6]

or, 80x - 240 = 3x² - 18x

or, 3x² - 18x - 80x + 240 = 0

or, 3x² - 98x + 240 = 0

or, 3x² - 90x - 8x + 240 = 0

or, 3x(x - 30) - 8(x - 30) = 0

or, (x - 30)(3x - 8) = 0

or, x = 30 or 8/3

time in fraction is not possible because the work done by Raju will be in negative which is not possible

∴ x = 30 hrs

Thus, Joseph will take 30 hrs to complete the work.

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Answer 2

Answer:

the work done by Joseph is 30 hours and Raju is 24 hours

Step-by-step explanation:

simple explanation

1. let [x] be time taken by Joseph and [x-6] be time taken by Raju.
2. let time taken by Joseph in one day = 1/x
3. let time taken by Raju in one day = 1/x-3
4. and total time taken by both to do same amount of work = 13(20) / 60
5. I.e = 40/3

slove them according to question

U will get equation as.

3x

$3x {}^{2} - 98x + 240 = 0$

then u will get answer as 30hrs and -8/3 will be rejected..

THNXX...