1. Stacy is painting her bedroom. She is able to paint 3/4 of the bedroom in 3 hours. At this rate, how long will it take her to paint the entire room?(1 point)
2. Miguel is returning from a trip. In 4 hours, he has driven 2/3 of the total distance. He wants to know how long the total drive will take. At this rate, what is the total time it will take him to reach his destination?(1 point)
3. Iris is asked to sweep the gymnasium floor after a basketball game. This requires her to push a sweeper from one end of the gym to the other and repeating the pattern until she has covered the entire floor. She completes 2/3 of the floor in 1/3 of an hour. At this rate, how long will it take her to complete the entire floor?(1 point)
To solve these problems, we need to find the time it will take for each person to complete the remaining fraction of the task.
1. Stacy is able to paint 3/4 of the bedroom in 3 hours. To find the time it will take her to paint the remaining 1/4 of the bedroom, we can set up a proportion. Let x represent the time it will take her to paint the entire room:
(3/4)/(3) = (1/4)/(x)
Cross-multiplying, we get:
(3/4) * x = (1/4) * 3
3x/4 = 3/4
Dividing both sides by 3/4, we get:
x = 1
So it will take Stacy 1 hour to paint the entire room.
2. Miguel has driven 2/3 of the total distance in 4 hours. To find the total time it will take him to reach his destination, we can set up a proportion. Let x represent the total time it will take him:
(2/3)/(4) = (1/3)/(x)
Cross-multiplying, we get:
(2/3) * x = (1/3) * 4
2x/3 = 4/3
Dividing both sides by 2/3, we get:
x = 2
So it will take Miguel 2 hours to reach his destination.
3. Iris completes 2/3 of the gymnasium floor in 1/3 of an hour. To find how long it will take her to complete the entire floor, we can set up a proportion. Let x represent the time it will take her:
(2/3)/(1/3) = (1)/(x)
Cross-multiplying, we get:
(2/3) * x = (1/3) * 1
2x/3 = 1/3
Dividing both sides by 2/3, we get:
x = 1/2
So it will take Iris 1/2 hour (or 30 minutes) to complete the entire floor.
1. To find out how long it will take Stacy to paint the entire room, we can set up a proportion. Let x be the total time it will take her.
We know that 3/4 of the room takes 3 hours, so we can set up the following proportion:
(3/4) / 3 = 1 / x
To solve for x, we can cross multiply:
(3/4) * x = 3
3x/4 = 3
Multiply both sides by 4 to get rid of the fraction:
3x = 12
Divide both sides by 3:
x = 4
Therefore, it will take Stacy 4 hours to paint the entire room.
2. To find out how long the total drive will take Miguel, we can set up a proportion. Let x be the total time it will take him.
We know that 2/3 of the total distance takes 4 hours, so we can set up the following proportion:
(2/3) / 4 = 1 / x
To solve for x, we can cross multiply:
(2/3) * x = 4
2x/3 = 4
Multiply both sides by 3 to get rid of the fraction:
2x = 12
Divide both sides by 2:
x = 6
Therefore, it will take Miguel 6 hours to reach his destination.
3. To find out how long it will take Iris to complete the entire floor, we can set up a proportion. Let x be the total time it will take her.
We know that 2/3 of the floor takes 1/3 of an hour, so we can set up the following proportion:
(2/3) / (1/3) = 1 / x
To solve for x, we can cross multiply:
(2/3) * x = 1
2x/3 = 1
Multiply both sides by 3 to get rid of the fraction:
2x = 3
Divide both sides by 2:
x = 3/2
Therefore, it will take Iris 3/2 of an hour or 1.5 hours to complete the entire floor.
1. To find out how long it will take Stacy to paint the entire room, we need to determine the amount of time it takes her to paint 1/4 of the room.
Since 3/4 of the room takes Stacy 3 hours to paint, we can set up a proportion:
(3/4) room / 3 hours = (1/4) room / x hours
Cross-multiplying, we get:
(3/4) * x hours = 3 hours * (1/4)
Simplifying, we have:
3x = 3(1/4)
3x = 3/4
Dividing both sides by 3, we find:
x = 1/4
Therefore, it will take Stacy 1/4 hour (or 15 minutes) to paint the remaining 1/4 of the room.
2. Similar to the first question, we can set up a proportion to find out the total time it will take Miguel to reach his destination.
Since 2/3 of the total distance takes Miguel 4 hours to drive, we have:
(2/3) distance / 4 hours = (1/3) distance / x hours
Cross-multiplying, we get:
(2/3) * x hours = 4 hours * (1/3)
Simplifying, we have:
2x = 4(1/3)
2x = 4/3
Dividing both sides by 2, we find:
x = 2/3
Therefore, it will take Miguel 2/3 hour (or 40 minutes) to reach his destination.
3. To determine how long it will take Iris to complete the entire gymnasium floor, we need to find out the amount of time it takes her to complete 1/3 of the floor.
Since she completes 2/3 of the floor in 1/3 hour, we can set up a proportion:
(2/3) floor / (1/3) hour = (1/3) floor / x hours
Cross-multiplying, we get:
(2/3) * x hours = (1/3) hour * (1/3)
Simplifying, we have:
2x = 1/3
Dividing both sides by 2, we find:
x = 1/6
Therefore, it will take Iris 1/6 hour (or 10 minutes) to complete the entire floor.