Another approach for questions like this is to assign a nice value to the job

Given: it takes three days for 10 workers to finish building one house
A nice number that works well with the numbers 3 and 10 is 30 (30 is the least common multiple of 3 and 10)
So, let's say one house has 30 rooms.
In other words, building ONE house requires the workers to build 30 rooms.

If 10 workers can build 30 rooms (aka one house) in 3 days, then in 1 day, the 10 workers can build 10 rooms.
If 10 workers can build 10 rooms in ONE DAY, then 1 worker can build 1 room in ONE DAY

How many days will it take 15 workers to finish four houses?
Our goal is to build 4 houses, which is the same as building 120 ROOMS
If 1 worker can build 1 room per day, then 15 workers can build a total of 15 rooms per day.
So, the number of days to build 120 ROOMS = 120/15 = 8 days

Answer: 8

I just used dimensional analysis (converting values using multiplication and cancelling of units).

This is a very complicated question. I would elevate it to HARD difficulty. It's certainly not a medium question by any means. Takes multiple leaps of logic to figure this out. Change the difficulty, please.

84% success rate ≠ HARD

Ok, NOW I got it, and I didn't even use any of your explanations above because I honestly couldn't understand them. Here it goes, and I set up proportions:

10 workers to build one house in 3 days. Work = rate x time. 1 house = r(3 days). So the rate for 10 workers is 1 house every 3 days (r = 1/3). Then set up the proportion:

Workers/rate = workers/rate. 10 workers / (1/3) = 15 workers / (rate). Solve for the rate to get 1/2. So in other words, 15 workers can build 1 house in 2 days. Now we can answer the question "how many days will it take 15 workers to finish four houses?" If 1 house takes 2 days for 15 workers, then 4 houses take 8 days. bingo.

It's lovely when I can finally see it and provide a more streamlined explanation than the ones offered above. I never cease to amaze myself!

for 10 workers 3 days to complete 1 house.
then, for 1 workers 3*10 =30 days to complete 1 house.
now ,if 1 workers can finish 1 house in 30 days,
then for 1 workers to finish 4 house tooks 4*30=120 days
so far, 1 workers 4 house 120 days ,
then 15 workers 4 house 120/15=8 days.

A student asked me to solve this in a different way, so here goes:

Given: It takes 3 days for 10 workers to finish building one house
Rate = output/time = 1/3
So, the 10 workers (combined) complete 1/3 of a house in one day.
This means ONE worker can complete 1/30 of a house in one day.
In other words, EACH worker's rate is 1/30 of a house per day.

How many days will it take 15 workers to finish four houses?
If EACH worker's rate is 1/30 of a house per day, then the combined rate of 15 workers = (1/30)(15) = 1/2
This means the TEAM of 15 workers has a combined rate of 1/2 houses per day.

Time = output/rate = 4/(1/2) = 8 days.

Thanks Brent GreenlightTestPrep