vishuboy wrote:

It takes 4 cooks 4 hours to bake 4 cakes. Assumingno change of rate, how many hours will it take 8 cooks to bake 8 cakes?

I really can't solve this problem. I am having problem in approach.

Every time I see work problems I am stuck in approach.

In this question, I was approaching like

\(\frac{1}{4*4*4}\)

calculating the cakes baked by 1 cook in 1 hour. I don't even know if I am right.

but now I am stuck can anyone help me.

Attachment:

WRTvariation.png [ 17.23 KiB | Viewed 2907 times ]
The resources

Bunuel listed are

very helpful.

I don't know exactly where you are lost. (No, you are not correct about individual rate, but you are very close!)

There is one basic approach that might help.

Use the standard RT=W formula, but add "number of workers" (or machines, etc.) to the left hand side of that formula.

See the table above. It is a standard RTW table, but one column has been added: # of workers.

We can manipulate RT=W. We can manipulate, exactly the same way,

#*R*T = WFirst we need individual rate at which the bakers work, i.e. how many cakes per hour does an individual baker make?

We get that rate from the first scenario. Then we use that rate to solve the second scenario.

1. Find individual rate from first scenario

Manipulate the equation from above

(# of workers) * r * t = W# of workers = 4

Rate = ??

Time = 4

Work = 4

Plugging into the formula: 4 * Rate * 4 = 4

Rate = \(\frac{4}{(4 * 4)}\) = \(\frac{1}{4}\)

(The rate is in cakes/hour. )

2. Use that individual baker rate, and manipulate the equation again for the second scenario. This time you need to find time.

Basic equation once more is

(# of workers) * r * t = W rate of individual worker =\(\frac{1}{4}\)

# of workers = 8

Work = 8

Plugging into equation:

\(8 * \frac{1}{4} * time = 8\)\((\frac{8}{4})(Time) = 8\)\(2*(Time) = 8\)Time = 4 hoursHope that helps.