Problem Solving

22/15.. pretty easy!!!

my take: d ..easy one

x needs 12 hrs to do the job
y and z needs = 1/(1/15 + 1/18) = 90/11

x : y+z = 12/(90/11) = 12*11/90 = 22/15

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.

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.

I don't understand the part where you flipped the 270/33. Why do you need o take the reciprocal?

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

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

22/15

Crazy that this post is still getting responses after 5 years!

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

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

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

Answer D)

Explanation:

For x: 1/12

For y and z combined: 1/15 + 1/18

Ratio x/(y+z) = (1/12)/(1/15 + 1/18)

After you do the math it comes to 15/22.

Flip this and you'll get the time taken to do the whole job which comes to 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?

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?

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.