Richard takes 35 minutes to mow a lawn, but with the help of his friend Joe it only took him 15 minutes. If Joe worked alone, how long would it take Joe to mow the same lawn?
If it takes Joe x minutes alone, then
1/35 + 1/x = 1/15
To find out how long it would take Joe to mow the same lawn alone, we can set up a rate equation. Let's assume that Richard's mowing rate is R, measured in lawns per minute, and Joe's mowing rate is J, also measured in lawns per minute.
We know that Richard takes 35 minutes to mow the lawn alone, so we can say that his mowing rate is:
R = 1 lawn / 35 minutes
With Joe's help, Richard completes the same job in 15 minutes. So, together their combined mowing rate is:
(R + J) = 1 lawn / 15 minutes
Now, we need to find Joe's mowing rate when he works alone, so we can subtract Richard's rate from the combined rate:
J = (R + J) - R
J = 1 lawn / 15 minutes - 1 lawn / 35 minutes
To simplify this equation, we need to find a common denominator:
J = (35 - 15) lawns / (15 * 35) minutes
J = 20 lawns / 525 minutes
Now dividing these two numbers, we can calculate Joe's mowing rate:
J ≈ 0.0381 lawns / minute
Therefore, it would take Joe approximately 26.17 minutes (1 lawn / 0.0381 lawns per minute) to mow the same lawn alone.