Problem Solving

I'm usually good with rate problems, this one has got me confused. How do I set this up? I'm comfortable with the pie method or the chart method. Thanks in advance for the help.

Caroline's and Carl's Cupcakes receive an order for a certain number of cupcakes. Caroline takes eight hours to complete a fraction of the order while Caroline's partner, Carl, takes sixteen hours to complete the rest of the order. How many hours would it take for Caroline to complete the order alone if Caroline made four times as many cupcakes in eight hours as Carl made in sixteen hours?

jzw wrote:I'm usually good with rate problems, this one has got me confused. How do I set this up? I'm comfortable with the pie method or the chart method. Thanks in advance for the help.

Caroline's and Carl's Cupcakes receive an order for a certain number of cupcakes. Caroline takes eight hours to complete a fraction of the order while Caroline's partner, Carl, takes sixteen hours to complete the rest of the order. How many hours would it take for Caroline to complete the order alone if Caroline made four times as many cupcakes in eight hours as Carl made in sixteen hours?

There are two fractions of order completed by Caroline and Carl, let's denote them A and B, they sum up to the total of one (1) complete order for a certain number of cupcakes, A+B=1.
Their speeds are A/8 Caroline's and B/16 Carl's. The relationship between A and B is further given as 8*(A/8)=4*16(B/16) or A=4B. To find time, within which Caroline completes the order alone, we need to define the fraction of work completed by her.

A=4B
A+B=1

5B=1 and B=1/5, hence A=4/5. The fraction of work completed by Caroline is 4/5.

If 4/5th fraction of work takes Caroline 8 hours, then
1 (one, i.e. complete) work will take her t hours

find t?
t=8:4/5=10 hours

answer 10 hours

jzw wrote:I'm usually good with rate problems, this one has got me confused. How do I set this up? I'm comfortable with the pie method or the chart method. Thanks in advance for the help.

Caroline's and Carl's Cupcakes receive an order for a certain number of cupcakes. Caroline takes eight hours to complete a fraction of the order while Caroline's partner, Carl, takes sixteen hours to complete the rest of the order. How many hours would it take for Caroline to complete the order alone if Caroline made four times as many cupcakes in eight hours as Carl made in sixteen hours?

Let Carl's rate = 2 cupcakes in 16 hours.
Since Caroline produces 4 times the number of cupcakes in 8 hours, Caroline's rate = 8 cupcakes in 8 hours = 1 cupcake per hour.
Total number of cupcakes = cupcakes produced by Caroline in 8 hours + cupcakes produced by Carl in 16 hours = 8+2 = 10.
Time for Caroline alone to produce 10 cupcakes = w/r = 10/1 = 10 hours.

GMATGuruNY wrote:

jzw wrote:I'm usually good with rate problems, this one has got me confused. How do I set this up? I'm comfortable with the pie method or the chart method. Thanks in advance for the help.

Caroline's and Carl's Cupcakes receive an order for a certain number of cupcakes. Caroline takes eight hours to complete a fraction of the order while Caroline's partner, Carl, takes sixteen hours to complete the rest of the order. How many hours would it take for Caroline to complete the order alone if Caroline made four times as many cupcakes in eight hours as Carl made in sixteen hours?

Let Carl's rate = 2 cupcakes in 16 hours.
Since Caroline produces 4 times the number of cupcakes in 8 hours, Caroline's rate = 8 cupcakes in 8 hours = 1 cupcake per hour.
Total number of cupcakes = cupcakes produced by Caroline in 8 hours + cupcakes produced by Carl in 16 hours = 8+2 = 10.
Time for Caroline alone to produce 10 cupcakes = w/r = 10/1 = 10 hours.

Hi Mitch,

Would you be able to help me here? I normally would solve the work-based problems using the method you have given here -- i.e. plugging in.

However, I tried to do this using rtw or chart method. and i get a different answer, not sure. pls can check if this is correct?

assuming carolina is A and her partner is B, lets say B's rate is x, and its given that A's rate 4 times B's ==> A's rate = 4x; thus the below table

------- A ------- B
R------ 4x ------ x
T------ 8 ------- 16
W------ 32x------ 16x

it follows that total work done is 48x. now is A is to do the entire work alone then let t be the time. rt = w; 4xt = 48x ==> t = 12.

what is wrong here, pls help. thanks.

Sorry to bother. I just realised my imbecility. Instead of work, i was trying match up the 4 times to rate. Corrected in the below now.

LeoBen wrote:

GMATGuruNY wrote:

jzw wrote:I'm usually good with rate problems, this one has got me confused. How do I set this up? I'm comfortable with the pie method or the chart method. Thanks in advance for the help.

Caroline's and Carl's Cupcakes receive an order for a certain number of cupcakes. Caroline takes eight hours to complete a fraction of the order while Caroline's partner, Carl, takes sixteen hours to complete the rest of the order. How many hours would it take for Caroline to complete the order alone if Caroline made four times as many cupcakes in eight hours as Carl made in sixteen hours?

Let Carl's rate = 2 cupcakes in 16 hours.
Since Caroline produces 4 times the number of cupcakes in 8 hours, Caroline's rate = 8 cupcakes in 8 hours = 1 cupcake per hour.
Total number of cupcakes = cupcakes produced by Caroline in 8 hours + cupcakes produced by Carl in 16 hours = 8+2 = 10.
Time for Caroline alone to produce 10 cupcakes = w/r = 10/1 = 10 hours.

Hi Mitch,

Would you be able to help me here? I normally would solve the work-based problems using the method you have given here -- i.e. plugging in.

However, I tried to do this using rtw or chart method. and i get a different answer, not sure. pls can check if this is correct?

assuming carolina is A and her partner is B, lets say B's produce or work done is x, and its given that A's produce is 4 times B's ==> A's work = 4x; thus the below table

------- A ------- B
R------ x/2 ------ x/16
T------ 8 ------- 16
W------ 4x------- x

it follows that total work done is 5x. now as A is to do the entire work alone then let t be the time. rt = w; (x/2)t = 5x ==> t = 10.

what is wrong here, pls help. thanks.