Bryan and Kim are painting a house. Working together they can paint a house in three-fifths the time it takes Kim to paint the house working alone. Bryan takes 15 hours to paint the house alone. How long does it take Kim to paint the house working alone?
let Kim's time working alone be x hrs
then Kim's rate = job/x
Brian's rate = job/15
combined rate = job/x + job/15 = job(x+15)/(15x)
time taken working together = job ÷ [job(x+15)/(15x)]
= 15x/(x+15) hrs
but 15x/(x+15) = (3/5)x
3x^2 + 45x = 75x
3x^2 - 30x = 0
3x(x - 10) = 0
x = 0 or x = 10, but clearly x > 0
so x = 10
It would take kim 10 hours to work alone.
check: combined rate = job(1/10 + 1/15) = job(1/6)
so the combined time = 6/1 = 6 hours
what is 3/5 of 10 ?
yes, 6 hours.
To solve this problem, let's break it down step by step.
Let's assume Kim takes "x" hours to paint the house working alone.
According to the problem, working together, Bryan and Kim can paint the house in three-fifths the time it takes Kim to paint the house working alone.
So, the time it takes them to paint the house together is (3/5)x hours.
We are also given that Bryan takes 15 hours to paint the house alone.
Now, let's set up an equation using the rates at which they paint the house:
Bryan's rate: 1 house / 15 hours
Kim's rate: 1 house / x hours
Their combined rate: 1 house / ((3/5)x) hours
Since they are working together, their combined rate is the sum of their individual rates. So, we can write the equation as:
1/15 + 1/x = 1/((3/5)x)
To solve for x, we need to find a common denominator. In this case, we can multiply the equation by 15x((3/5)x) to simplify the equation:
5x + 15(3/5)x = 15(3/5)x
Simplifying further:
5x + 9x = 9x
14x = 9x
Subtracting 9x from both sides:
14x - 9x = 0
5x = 0
Dividing both sides by 5:
x = 0
Here we have encountered a problem. We cannot have x = 0 as the time it takes for Kim to paint the house. This means that the information given in the problem is conflicting or incorrect, as it leads to an impossible solution. Please double-check the problem statement or provide additional information if possible.