Person A makes 300 cakes in 2 hours. Person B makes 300 cakes in 2 hours. Person C makes 300 cakes in 3 hours

How long does it take all 3 working together to make 300 cakes. (Assume no synergies and rates are additive. So Person A and Person B would make 600 cakes in 2 hours together).

So I wasn't sure what to do here so I tried to figure out the per hour rate of each.

Person A makes 150 cakes in an hour. Person B makes 150 cakes in an hour. Person C makes 100 cakes in an hour.

So that wasn't getting me anywhere. All I know is that in an hour, they all make 150+150+100 = 400 cakes. So, to make 300 cakes, they need less than 1 hour.

  • $\begingroup$ Common-denominator $6$ hours, then $R_A=\frac {900\text {cakes}}{6\text{hours}}$, $R_B=\frac {900\text {cakes}}{6\text{hours}}$, $R_C=\frac {600\text {cakes}}{6\text{hours}}$ and $R_A+R_B+R_C=\frac {2400\text {cakes}}{6\text{hours}}=\frac {100\text{cakes}}{0.25\text{hours}}$, multiply by $3$ to get $300$ cakes in... $\endgroup$ – abiessu Jan 30 '14 at 20:27
  • $\begingroup$ You should have kept going with, to paraphrase you, "they make 400 cakes per hour". $\endgroup$ – David Mitra Jan 30 '14 at 20:30

Let's back up and go back to your observation, and complete the thought:

If together they are able to make $400$ cakes in an hour, then to make $300$ cakes takes them $$\dfrac{300}{400} \text{hours} = 45\text{ min}$$

We can also setup the problem as one of ratios: $$\dfrac{400}{1 \text{hour}} = \frac {300}{x\text{ hours}}$$ and then solve for $x$


Another way to tackle it is, you can think of work problems like distance problems. Just like ratetime=distance, ratetime=work

When you have several people working together, you add their rates together. You did a great job of finding this, so we know that they make 400cakes/hour (which is their rate together) to find out how long it takes them to make 300 cakes we use the work equation and solve for t (time) 400c/h*t=300

so like was said before, t=3/4 of an hour or 45 minutes


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.