Question

Working alone, john can do a job in 9 days. harry could do the same job in 7 days. assuming a day has 8 hours, how many hours will it take them working together to do the job, assuming their productivity does not change working together

Answer 1

Answer : Harry and John can do the job in 31.50 hours, assuming their productivity doesn't change.

We follow these steps to arrive at the answer:

Number of days taken by John : 9

Number of days taken by Harry : 7

Number of working hours per week =8 hours

$Number of hours required by John = 72 (9 *8)$

$Number of hours required by John = 56 (7 *8)$

Since both Harry and John are working on the same product, let 'x' be the time spent by each person on the job.

Since both Harry and John have to finish only one product working together, let the sum of both their efforts be 1.

We can write the equation as:

$\frac{x}{72}+ \frac{x}{56} =1$

Since the LCM of 72 and 56 is 504, we multiply the first term by 7 and the second by 9. After this the equation can be re-written as:

$\frac{7x}{504}+\frac{9x}{504} =1$

$16x =504$

$x = 31.50 hours$