It takes Ted 20 minutes to paint a wall. Burt can paint the same wall in 30 minutes. How long will it take for the two of them to do the job together?
Well, if Ted takes 20 minutes to paint a wall and Burt takes 30 minutes, then together they would probably take... well, let's just say they might have some "paintful" teamwork. But fear not! We can solve this puzzling partnership problem!
To find out how long it would take for them to complete the job together, we can use a mathematical comedic trick known as the "harmonic mean." It sounds fancy, but don't worry, it's just like a magic trick with numbers!
So, to calculate the harmonious harmony of their painting skills, we'll take the reciprocal of their individual times. Ted's reciprocal would be 1/20 (since he takes 20 minutes) and Burt's reciprocal would be 1/30 (since he takes 30 minutes).
Now, just add these two reciprocals together: 1/20 + 1/30 = 3/60 + 2/60 = 5/60.
And now, for the grand finale, we'll perform one final mathematical magic trick! Take the reciprocal of our sum: 60/5 = 12.
So, it will take Ted and Burt approximately 12 minutes to finish painting the wall together! Ta-da!
To find out how long it will take for Ted and Burt to paint the wall together, we can use the concept of work rates.
First, we need to determine the individual work rates for Ted and Burt. Work rate is the amount of work done per unit of time. In this case, the work is painting the wall, and the unit of time is minutes.
Ted takes 20 minutes to paint the wall, so his work rate is 1 wall / 20 minutes, which can be simplified to 1/20 wall per minute.
Similarly, Burt takes 30 minutes to paint the wall, so his work rate is 1 wall / 30 minutes, or 1/30 wall per minute.
To determine how long it will take for them to paint the wall together, we can add up their individual work rates. So their combined work rate is 1/20 + 1/30 wall per minute.
To add these fractions together, we need a common denominator. The least common multiple of 20 and 30 is 60.
So we can rewrite the fractions with the common denominator:
1/20 wall per minute = 3/60 wall per minute
1/30 wall per minute = 2/60 wall per minute
Now we can add the fractions:
3/60 + 2/60 = 5/60 wall per minute
Since the combined work rate is 5/60 wall per minute, it will take them 60/5 = 12 minutes to paint the wall together.
Therefore, it will take Ted and Burt 12 minutes to paint the wall together.