Exercises: Compound proportion

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

An animal shelter needs $480$ kg of feed to feed $40$ dogs for $30$ days. If the shelter receives a donation and increases its capacity to $60$ dogs, how many kilograms 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 to the same server using $5$ identical connections, how many minutes will it take?

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

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

Five decorative water fountains, with the same flow rate, consume $300$ liters of water if they are turned on for $8$ hours. Calculate how many liters $10$ 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 hire $2$ more vans to boost the service, how many parcels will they be able to deliver in a period of $3$ days?

To illuminate an art exhibition hall for $12$ days, $15$ low-energy LED spotlights generated an expense of $54$ pesos. What will the electricity cost be if $20$ identical spotlights are used during an event lasting $10$ days?

A group of $4$ travel content creators managed to edit $12$ videos for their channel working $6$ hours a day for a week. If $2$ more collaborators join the team next month and 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 at a city farm for $12$ days, $540$ kg of feed was required. Thanks to a new grant, the farm has acquired $5$ more cows. How many kilograms of feed will be needed to feed all the animals for $20$ days?

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

A team of $6$ municipal workers cleans a beach area of $1500$ $m^2$ in $5$ hours. For the next cleaning day, the municipality has $8$ workers, but the area to be cleaned is $2800$ $m^2$. Calculate how long it will take them to finish the job.

In an electronics components factory, $5$ identical machines produce $2000$ processors running for $8$ 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 per day must all the machines run?

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

To print $1200$ advertising posters, $4$ industrial printers have been running 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 excavated a $60$-meter section of an ancient Roman road working for $9$ days at a rate of $7$ hours per day. If they want to excavate another $80$-meter section in $14$ days, how many hours per day must they work if the team keeps the same number of people?

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

A municipal cleaning team, consisting of $12$ workers, managed to clean an area of $3,600\text{ m}^2$ of woodland in $6$ days, working $8$ hours per day. For next week, the municipality needs to clean an area of $5,000\text{ m}^2$. If $3$ workers are out sick and cannot attend, how many hours per day must the remaining workers work to finish the task in only $5$ days?

A video game server farm uses $8$ cooling units to maintain the optimal temperature for $120$ servers running for $24$ hours a day, with an electricity cost of $\text{RD\$}\ 480$ a week. If the company decides to expand its capacity to $200$ servers and the price of electricity rises, so that the maximum allowed cost is $\text{RD\$}\ 600$, for how many hours a day can the servers be switched on if the same $8$ cooling units are kept? (Assume 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 it take the remaining printers to print $6,000$ copies if, to compensate for the missing 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 required).

A group of $5$ identical taps takes $8$ hours to fill $3$ tanks of $600$ liters each. If we want to fill $4$ tanks of $900$ liters each in a maximum time of $10$ hours, how many taps with the same characteristics will we need to turn on? If the result is not an integer, explain the minimum number of taps we should install.

Six tanker trucks of $12,000\text{ L}$ capacity each 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 it take them to complete the emptying if each truck makes $5$ trips per day?

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

A sports footwear factory 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 only $8$ days. If they bought $3$ additional machines with the same characteristics, how many extra hours per day, above the usual $16$, will all the machines have to run to meet the deadline?