A group of college students is volunteering for Help the Homeless during their spring break. They are putting the finishing touches on a house they built. Working alone, Irina can paint a certain room in 8 hours. Paulo can paint the same room in 7 hours. Write an equation that can be used to find how long it will take them working together to paint the room. How many hours will it take them to paint the room? How many hours will it take them to paint the room? If necessary, round your answer to the nearest hundredth.
A. 8/x + 7/x = 1; 15 hours
B. 1/8 + 1/7 = 1/x; 7.5 hours
C. x/8 + x/7 = 1; 3.73 hours
D. x/8 + x/7 = 1; 1.87 hours
I think it's C, but can one of you lovely tutors confirm! Hope all is well x
looks good
Well, aren't you just canvas-ing for confirmation? Allow me to paint you a picture.
Let's say x represents the number of hours it will take them working together to paint the room. Since Irina can paint in 8 hours and Paulo can paint in 7 hours, we can set up the equation (1/8)x + (1/7)x = 1 to find the combined rate of painting. Combining those fractions, we get (15/56)x = 1.
To solve for x, we multiply both sides of the equation by the reciprocal of (15/56), which is (56/15). Multiplying these values, we find that x = (56/15) hours.
Well, it looks like you're quite the painter-pretender! You were correct! So, in C, it will take them approximately 3.73 hours to paint the room together. Keep up the great work, and remember to brush up on those equations!
Hi! You are correct, the equation that can be used to find how long it will take them to paint the room together is:
x/8 + x/7 = 1
To solve for x, you can find a common denominator, which is 56 in this case. Multiplying both sides of the equation by 56 gives:
7x + 8x = 56
Combining like terms:
15x = 56
Dividing both sides of the equation by 15 gives the value of x:
x = 56/15
To find the answer in hours, you can divide 56 by 15, which is approximately 3.73.
Therefore, the correct answer is C. It will take them approximately 3.73 hours to paint the room together.
To solve this problem, we can use the concept of "work rate." The work rate represents the amount of work done per unit of time.
Let's say Irina's work rate is R1 (the amount of work she can do in 1 hour) and Paulo's work rate is R2. We can find their individual work rates by taking the reciprocal of the time it takes for them to complete the task. So, Irina's work rate is 1/8 (since she can complete the task in 8 hours) and Paulo's work rate is 1/7 (since he can complete the task in 7 hours).
Now, we need to find the combined work rate when they work together. We add their work rates to get the total work rate when they work together. Let's call this combined work rate R.
R = R1 + R2
= 1/8 + 1/7
Now, we can set up the equation to find how long it will take them to complete the task together. Let's call the time it takes for them to complete the task together x.
1/x = R
= 1/8 + 1/7
To solve this equation, we need to find the value of x. Simplifying the right side of the equation, we get:
1/x = (7 + 8)/(8 * 7)
= 15/56
Now, let's solve for x by taking the reciprocal of both sides of the equation:
x = 56/15
So, it will take them approximately 3.73 hours to paint the room together. Therefore, the correct answer is C.