SOLUTION: three men can individually do a job in 5,6 and 7 hours respectively . what fractions of the entire job is done by the three men together in 1 hour ?

Question 1095128: three men can individually do a job in 5,6 and 7 hours respectively . what fractions of the entire job is done by the three men together in 1 hour ?
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
rate * time = quantity

the quantity is equal to 1 job.

therefore rate * time = 1

for the first person, the equation becomes rate * 5 = 1
rate for the first person is 1/5 of the job in 1 hour.

for the second person, the equation becomes rate * 6 = 1
rate for the second person is 1/6 of the job in 1 hour.,

for the third person, the equation becomes rate * 7 = 1
rate for the third person is 1/7 of the job in 1 hour.

when all 3 persons work together, their rates are additive.

their combined rate is (1/5 + 1/6 + 1/7) of the job in 1 hour.

place (1/5 + 1/6 + 1/7) under the common denominator of 210 and the combined rate becomes (42 + 35 + 30) / 210 = 107/210 of the job in 1 hour.

their combined rate is 107/210 of the job in 1 hour.

that's your solution.

to determine how long it takes to complete the job, you get:

r * t = q becomes 107/210 * t = 1

solve for t to get t = 1 / (107/210) = 1 * 210/107 = 210/107 hours.

the first person can do the job in 5 hours, therefore his rate is 1/5 of the job in 1 hour.
multiply that by 210/107 hours and he completes 1/5 * 210/107 = 42/107 of the job in 210/107 hours.

the second person can do the job in 6 hours, therefore his rate is 1/6 of the job in 1 hour.
multiply that by 210/107 hours and he completes 1/6 * 210/107 = 35/107 of the job in 210/107 hours.

the third person can do the job in 7 hours, therefore his rate is 1/7 of the job in 1 hour.
multiply that by 210/107 hours and he completes 1/7 * 210/107 = 30/107 of the job in 210/107 hours.

add up the contribution of each person and you get 42/107 + 35/107 + 30/107 = 107/107 of the job in 210/107 hours.

107/107 is equal to 1, therefore the whole job is completed in 210/107 hours.

210/107 hours is equal to 1.962616822 hours in decimal form.

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

three men can individually do a job in 5,6 and 7 hours respectively . what fractions of the entire job is done by the three men together in 1 hour?

Fastest can do the job in 5 hours, or of the job in 1 hour
Second fastest can do the job in 6 hours, or of the job in 1 hour
Slowest can do the job in 7 hours, or of the job in 1 hour
In 1 hour the 3 can do:
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