May takes 12 hours to type a report. Her friend helps her and together they finish the job in 4 hours. How long would it take her friend had she worked alone?
Representation:
Equation:
Solution:
Conclusion:
1/12 + 1/x = 1/4
x = 6
so, 6 hours for the friend.
What is the solution set of this inequality: x – 1 < 10? *
x>11
x<1
Option 5
x<11
x>10
Representation:
Let's represent May's typing speed as x (in reports per hour) and her friend's typing speed as y (in reports per hour).
Equation:
May's typing speed: x
May's time: 12 hours
May's work: x * 12
May's friend's typing speed: y
May's friend's time: t (unknown)
May's friend's work: y * t
Together, they finish the job in 4 hours:
May's work + May's friend's work = Job completed
x * 12 + y * 4 = 1
Solution:
Since the friend is helping May, they are working together, and we can determine their combined work rate.
May's work + May's friend's work = Job completed
x * 12 + y * 4 = 1
Solving the equation above, we can find the value of x + y:
12x + 4y = 1
y = (1 - 12x) / 4
To find out how long it would take May's friend to finish the job alone, we need to substitute the value of y into the equation:
May's friend's time = t
t = 1/y
Substituting the value of y:
t = 1 / ((1 - 12x) / 4)
Conclusion:
May's friend would finish the job alone in t = 1 / ((1 - 12x) / 4) hours.
Representation:
Let's assume that May's friend takes x hours to complete the report on her own.
Equation:
May takes 12 hours to type the report, so her work rate is 1/12 of the report per hour.
May and her friend, working together, finish the job in 4 hours, so their combined work rate is 1/4 of the report per hour.
If May's friend takes x hours to complete the report on her own, her work rate is 1/x of the report per hour.
May's work rate (1/12) + Her friend's work rate (1/x) = Combined work rate (1/4)
Solution:
To find x, we need to solve the equation:
1/12 + 1/x = 1/4
To do this, we can first convert the fractions to a common denominator:
1/12 + 1/x = (x + 12)/(12x) = 1/4
Cross-multiplying, we get:
4(x + 12) = 12x
Simplifying and solving for x:
4x + 48 = 12x
48 = 8x
x = 48/8 = 6
Conclusion:
It would take May's friend 6 hours to complete the report on her own.