P and Q individually completes a work in 15 and 25 days respectively.In How Mny Days P And Q Can Complete the work if they start working on alternate days. Starting From P And Q?

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Answer 1

P and Q individually completes a work in 15 and 25 days respectively.In How Mny Days P And Q Can Complete the work if they start working on alternate days. Starting From P And Q?

The "key" to understanding "work together" problems is to realize that rate may be either hours per job (that is, hr/job) or jobs per hour (that is, job/hr).

So, "P completes a work in 15 days" means 1/15 work/day or 15 days/work.

So, to complete 1 total work, if P and Q worked the same number of days, x,

x/15 + x/75 = 1

5x/75 + 3x/75 = 1

8x/75 = 1

x = 75/8

x = 9.375 days each

But, Q might have worked 1 day less than P., so

day who amt. total

------ ------ ----- -----

1 P 5/75 5/75

2 Q 3/75 8/75

3 P 5/75 13/75

4 Q 3/75 16/75

5 P 5/75 21/75

6 Q 3/75 24/75

7 P 5/75 29/75

8 Q 3/75 32/75

9 P 5/75 37/75

10 Q 3/75 40/75'

11 P 5/75 45/75

12 Q 3/75 48/75

13 P 5/75 53/75

14 Q 3/75 56/75

15 P 5/75 61/75

16 Q 3/75 64/75

17 P 5/75 69/75

18 Q 3/75 72/75 [9 days each]

19 P 5/75 77/75 [ 77/75 is more than 75/75 = 1, so 19 days does it.]

Or, you could have used 9.375 to get 9 days each plus a little bit. 9 days each (18 days total) is

9*5/75 + 9*3/75 = (45+27)/75 = 72/75 and it is P's turn next.

Thus, 19 days is (72+5)/75 = 77/75, which is greater than 1. The work is done.