Exercises: Compound proportion

In a clothing customization shop, $3$ heat press machines manage to print $120$ T-shirts working for $4$ hours. If, due to an urgent order from a school, $5$ identical machines are started up, how many T-shirts will they be able to print in $6$ hours?

An animal shelter needs $480$ pounds of feed to feed $40$ dogs for $30$ days. If the shelter receives a donation and increases its capacity to $60$ dogs, how many pounds of feed will they need to feed them for $20$ days?

To upload the files of a new video game to a server, $4$ identical fiber optic connections take $15$ minutes to transfer $120$ GB. If we want to transfer $200$ GB on the same server using $5$ identical connections, how many minutes will they take?

A group of $6$ friends decides to distribute flyers for their local e-sports team. In $3$ hours they have managed to post $450$ flyers. If next Saturday $2$ more friends join the group and they work for $4$ hours, how many flyers will they distribute in total?

In a water recycling plant, $8$ identical treatment plants filter $2400$ cubic feet of water over a period of $5$ days. How many cubic feet of water will $12$ treatment plants filter if they operate for $7$ days?

Five decorative water fountains, with the same flow rate, consume $300$ gallons of water if they are turned on for $8$ hours. Calculate how many gallons $10$ identical fountains will consume if they are kept on for only $2$ hours.

A courier company uses $4$ vans to deliver $640$ parcels in $5$ days. If the company decides to rent $2$ more vans to reinforce the service, how many parcels will they be able to deliver in a period of $3$ days?

To light an art exhibition hall for $12$ days, $15$ energy-saving LED spotlights have generated a cost of $\$54$. What will the electricity cost be if $20$ identical spotlights are used during an event lasting $10$ days?

A group of $4$ content creators specializing in travel has managed to edit $12$ videos for their channel working $6$ hours a day for a week. If for next month $2$ more collaborators join the team and they decide to work $8$ hours a day, how many videos will they be able to edit in the same period of time?

To feed the $15$ cows of a farm school for $12$ days, $540$ pounds of feed have been needed. Due to a new grant, the farm has acquired $5$ more cows. How many pounds of feed will be needed to feed all the animals for $20$ days?

A courier company uses $8$ drones to deliver $160$ packages in $4$ hours of flight. If the company decides to increase its fleet to $10$ drones and wants to deliver $250$ packages, how many total flight hours will the drones need to complete the task?

A team of $6$ municipal workers cleans an area of $1500$ $m^2$ of beach in $5$ hours. For the next cleaning day, the town council has $8$ workers, but the area to be cleaned is $2800$ $m^2$. Find how long they will take to finish the job.

In an electronic components factory, $5$ identical machines produce $2000$ processors working $8$ hours a day. Due to an urgent order, the factory must deliver $3500$ processors in the same number of days. If $2$ more machines are started up, how many hours a day must all the machines work?

Three identical faucets fill a $10$ $m^3$ tank in $6$ hours. If we want to fill a $25$ $m^3$ pond using $5$ faucets with the same flow rate as the previous ones, how many hours will we need?

To print $1200$ advertising posters, $4$ industrial printers have been working for $15$ hours. If one of the printers breaks down and we need to print $1800$ posters for a new campaign, how many hours must the remaining printers work?

A team of $12$ archaeologists has excavated a $60$-foot section of an ancient Roman road, working $9$ days at a rate of $7$ hours a day. If they want to excavate another $80$-foot section in $14$ days, how many hours a day must they work if the team keeps the same number of people?

In an animal shelter, it has been calculated that $15$ bags of feed of $20\text{ kg}$ each are enough to feed $40$ dogs for $12$ days. Due to a rescue campaign, the number of dogs increases by $20$ more animals. If the shelter buys $30\text{ kg}$ bags of the same feed, how many bags will they need to feed all the dogs for $25$ days?

A municipal cleaning brigade, made up of $12$ workers, has managed to clean an area of $3.600\text{ m}^2$ of forest in $6$ days, working $8$ hours a day. For next week, the city council needs to clean an area of $5.000\text{ m}^2$. If $3$ workers have taken sick leave and will not be able to attend, how many hours a day will the remaining workers have to work to finish the task in just $5$ days?

A video game server farm uses $8$ cooling units to maintain the optimal temperature of $120$ servers running for $24$ hours a day, with an electricity cost of $480\text{ \$}$ a week. If the company decides to expand its capacity to $200$ servers and the price of electricity rises, so that the maximum permitted cost is $600\text{ \$}$, for how many hours a day can the servers be turned on if the same $8$ cooling units are kept? (Consider that the cost is directly proportional to the number of servers and the hours of use).

To print the flyers for a music festival, $3$ industrial printers working simultaneously take $15$ hours to print $4.500$ copies. One of the printers breaks down and must be removed. How long will the remaining printers take to print $6.000$ copies if, to compensate for the lack of the third machine, the printing speed of the other two is increased by $25\text{ \%}$? (Hint: think about how the increase in speed affects the time needed).

A group of $5$ identical faucets takes $8$ hours to fill $3$ tanks of $600$ gallons each. If we want to fill $4$ tanks of $900$ gallons each in a maximum time of $10$ hours, how many faucets of the same characteristics will we need to open? If the result is not an integer, reason how many faucets we should install as a minimum.

Six tanker trucks of $12.000\text{ L}$ capacity each have made $4$ trips to empty an industrial waste container in $2$ days. If $2$ more trucks of $15.000\text{ L}$ capacity each are hired to do a similar job emptying a container that is $50\text{ \%}$ larger than the previous one, how many days will they take to complete the emptying if each truck makes $5$ trips a day?

A team of $4$ programmers has developed a mobile app of $180$ screens in $15$ days, dedicating $6$ hours a day each. For a new project of a more complex app of $300$ screens, the company has $20$ days. If they decide to hire $2$ more programmers and increase the working day to $8$ hours a day, calculate if they will be able to deliver the project on time and how many screens a day on average the whole team will now develop.

A sports footwear factory has produced $2.400$ pairs of sneakers in $10$ days working with $12$ automatic machines for $16$ hours a day. Due to an urgent order from an international distributor, the factory must produce $3.600$ pairs in just $8$ days. If they have bought $3$ additional machines of the same characteristics, how many extra hours a day, above the usual $16$, will all the machines have to run to meet the deadline?