John can build 7 birdhouses in 5 hours, write an equation that will allow john to calculate the time it will take to build any given number of houses. HOW MANY HOUSES in 40 hours? #2 How long will it take to build 35 houses?
To calculate the time it will take for John to build any given number of houses, we need to set up a proportional relationship between the number of houses and the time taken.
Let's first find the rate at which John builds birdhouses. We know that he can build 7 birdhouses in 5 hours. Therefore, his rate is 7 birdhouses / 5 hours, which can be simplified to 7/5 birdhouses per hour.
Now, let's represent the number of houses John wants to build as "x" and the time it will take as "t". Since we have established that his rate is 7/5 birdhouses per hour, we can set up a proportion:
7/5 = x/t
To solve for t, we can cross-multiply and solve:
7t = 5x
Now, let's answer your questions:
#1 How many houses can John build in 40 hours?
To find the number of houses, we need to solve the equation 7t = 5x for x when t = 40:
7 * 40 = 5 * x
280 = 5x
x = 280/5
x = 56
Therefore, John can build 56 houses in 40 hours.
#2 How long will it take to build 35 houses?
To find the time it will take, we need to solve the equation 7t = 5x for t when x = 35:
7t = 5 * 35
7t = 175
t = 175/7
t = 25
Therefore, it will take John 25 hours to build 35 houses.