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og math # 130
Use work formula and this problem takes > minute.
x = 12
y = 15
z = 18
need ratio of x to y + z
formula for work = 1 / individual hours y + 1 / individual hours z = 1 / combined hours to complete or reciprocal of your answer = 1/15 + 1/18. Use bowtie method to add fractions = 33/270 or 270/33 since you then need to take reciprocal. Need x over this so 12 over 270/33 = 12 x 33/270 = 396 / 270. Dont need to reduce only plausible answer is 22/15.
x = 12
y = 15
z = 18
need ratio of x to y + z
formula for work = 1 / individual hours y + 1 / individual hours z = 1 / combined hours to complete or reciprocal of your answer = 1/15 + 1/18. Use bowtie method to add fractions = 33/270 or 270/33 since you then need to take reciprocal. Need x over this so 12 over 270/33 = 12 x 33/270 = 396 / 270. Dont need to reduce only plausible answer is 22/15.
I don't understand the part where you flipped the 270/33. Why do you need o take the reciprocal?robvspencer wrote:Use work formula and this problem takes > minute.
x = 12
y = 15
z = 18
need ratio of x to y + z
formula for work = 1 / individual hours y + 1 / individual hours z = 1 / combined hours to complete or reciprocal of your answer = 1/15 + 1/18. Use bowtie method to add fractions = 33/270 or 270/33 since you then need to take reciprocal. Need x over this so 12 over 270/33 = 12 x 33/270 = 396 / 270. Dont need to reduce only plausible answer is 22/15.
Since we know Work = Rate X Time
work done is same by x,y,z i.e. lets say work done is 1
Rate at which x works Rx-----1/12
similarly Ry-----1/15
Rz-----1/18
When y and z work together their rate of doing a job...Ry+Rz-----1/15+1/18=11/90
Now Tx/Ty+z=Ry+z/Rx since work done is same, time is inversely proportional to rate.
Tx/Ty+z=(11/90)/(1/12)=11*12/90=22/15
Thanks
work done is same by x,y,z i.e. lets say work done is 1
Rate at which x works Rx-----1/12
similarly Ry-----1/15
Rz-----1/18
When y and z work together their rate of doing a job...Ry+Rz-----1/15+1/18=11/90
Now Tx/Ty+z=Ry+z/Rx since work done is same, time is inversely proportional to rate.
Tx/Ty+z=(11/90)/(1/12)=11*12/90=22/15
Thanks
Rate of work for x is 1/12 i.e. it will complete 1/12th of work in one hour
Rate of work for y is 1/15 i.e. it will complete 1/15th of work in one hour
Rate of work for z is 1/18 i.e. it will complete 1/18th of work in one hour
Combined rate of work for y & z is 1/15 + 1/18 =(18 + 15 )/270 = 11/90
i.e. both complete 11/90th of work in one hour
So total time taken by both of them to complete the work is 90/11
SO ratio of time taken by X & by y & Z together =12/(90/11)
=22/15
Rate of work for y is 1/15 i.e. it will complete 1/15th of work in one hour
Rate of work for z is 1/18 i.e. it will complete 1/18th of work in one hour
Combined rate of work for y & z is 1/15 + 1/18 =(18 + 15 )/270 = 11/90
i.e. both complete 11/90th of work in one hour
So total time taken by both of them to complete the work is 90/11
SO ratio of time taken by X & by y & Z together =12/(90/11)
=22/15
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Amount of work done by printer X in 1 hour = 1/12
Amount of work done by printer Y in 1 hour = 1/15
Amount of work done by printer Z in 1 hour = 1/18
Work done by Y & Z in 1 hour = ((1/15)+(1/18))
= (11/90)
SO actual time taken by Y & Z together = 90/11
ratio of X/ (Y + Z) = 12 / (90/11)
= 2/(15/11)
= 22/15
Amount of work done by printer Y in 1 hour = 1/15
Amount of work done by printer Z in 1 hour = 1/18
Work done by Y & Z in 1 hour = ((1/15)+(1/18))
= (11/90)
SO actual time taken by Y & Z together = 90/11
ratio of X/ (Y + Z) = 12 / (90/11)
= 2/(15/11)
= 22/15
The Biggest hurdle in the Path of success is the fear of failure
Y and Z together do the job in
1/15 + 1/18 = 11/90
Therefore, Y and Z together do the job in 90/11 hours
12 : 90/11
which is 22:15
1/15 + 1/18 = 11/90
Therefore, Y and Z together do the job in 90/11 hours
12 : 90/11
which is 22:15
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Bharat
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Bharat
If you find my post helpful, please click on the 'Thank' icon.
Time taken for x = 12 hrs
Time taken for y = 15 hrs
Time taken for z = 18 hrs
Let the time taken for both y and z to complete the task = t
therefore, 1/t = 1/15 + 1/18 = 11/90
hence, t = 90/11
therefore, x:t = 12/90/11 = (12*11)/90 = 22/15
Time taken for y = 15 hrs
Time taken for z = 18 hrs
Let the time taken for both y and z to complete the task = t
therefore, 1/t = 1/15 + 1/18 = 11/90
hence, t = 90/11
therefore, x:t = 12/90/11 = (12*11)/90 = 22/15
Doesn't this solution imply that x is faster than y and z combined? This seems counter intuitive. x:y&z
22:15?
22:15?
I'll explain. No, x is taking 22 hrs as per the solution vs 15 for y and z. X is slower than y and z combined.kingkavalli wrote:Doesn't this solution imply that x is faster than y and z combined? This seems counter intuitive. x:y&z
22:15?
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