Compound proportion

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?

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

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

In a water recycling plant, $8$ identical treatment units filter $2400$ cubic metres of water over a period of $5$ days. How many cubic metres of water will $12$ treatment units filter if they run for $7$ 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 paint the fences of a municipal sports centre, a crew of $3$ people took $8$ days working $6$ hours a day. The town council commissions an identical job to another crew made up of $6$ people who will work $4$ hours a day. Lucas solved the problem by writing the following in his notebook:

"Since there are twice as many people and fewer hours per day, I set up the proportion: $x = 8 \times \frac{6}{3} \times \frac{6}{4} = 24$ days".

1. a) Without performing numerical calculations, explain why a result of $24$ days is inconsistent with common sense in this case.
2. b) Identify the conceptual mistake Lucas made when analysing the relationship of each magnitude with the number of days.
3. c) Correct the approach and calculate the exact number of days the new crew will need to finish the job.

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?

In an animal rescue centre, 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 centre 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 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 $€480$ 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 $€600$, 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).

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?

A group of $5$ identical taps takes $8$ hours to fill $3$ tanks of $600$ litres each. If we want to fill $4$ tanks of $900$ litres 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.