# Two students clean 5 rooms in 4 hours. How long do 40 students need for 40 rooms?

A class decides to do a community involvement project by cleaning classrooms in a school. If 2 students can clean 5 classrooms in 4 hours, how long would it take for 40 students to clean 40 classrooms?

• Have you studied ratios and proportions? Jun 17, 2013 at 19:26
• I do but I'm always lost when it comes to this types of question, seems like what they say is true, math need practice Jun 17, 2013 at 19:30

A student-hour is a unit of work. It represents 1 student working for an hour, or 60 students working for one minute, or 3600 students working for 1 second, or ...

You're told that cleaning 5 classrooms takes 2 students 4 hours, or $8$ student-hours. So one classroom takes $\frac{8}{5}$ or $1.6$ student-hours.

So the 40 classrooms will take $40 \times 1.6$ or $64$ student-hours.

The forty students will put out $64$ student-hours in $\frac{64}{40}$ or $1.6$ hours...

• +1 for using the concept of"Unit of Work"! Breaking down something so simple to meaningful reusable concepts shows deep insight. It seemed like a any other simple question but the answer is really different. Jun 17, 2013 at 23:20

Hint: the theory is that everybody can work in parallel with full efficiency. So if you put $40$ students on those $5$ classrooms, how long would it take? Then you have $8$ times that many classrooms.....

Two students clean $\,5\,$ rooms in $\,4\,$ hours, which means they both clean $\,\frac54\,$ of a room per hour, and this means each student cleans $\,\frac58\,$ of a room per hour. Thus, $\,40\,$ students clean $\,40\cdot\frac58=25\,$ rooms per hour, which means they all together need for $\,40\,$ rooms

$$\color{red}{\frac{40}{25}=\frac85=1\;\text{hour and \,36\, minutes}}\,$$

• Ah, your comment came in after my edit. Check now, I made a typo and "respected it" all along the answer...:) Jun 17, 2013 at 23:52
• You flipped the numbers: they both clean 5/4 rooms per hour and one then cleans 5/8 rooms per hour. Forty students can thus clean 200/8 rooms per hour or 25 rooms per hour. To clean 40 rooms then takes 40/25 or 1.6 hours, in agreement with all of the above answers. Jun 17, 2013 at 23:52
• Yes, that was a typo all along .Already corrected, thank you both. Jun 17, 2013 at 23:53