Dal and kim can assemble a swing set in 1.5 hours. working alone it takes kim 4 hour longer than dal how long will it take dal alone to assemble the swing set
dan's rate -- swing/x , where x is the numbers of hours to assemble the swing by himself
kim's rate --- swing/(x+4)
so swing/x + swing/(x+4) = swing/1.5
divide by "swing"
1/x + 1/(x+4) = 1/1.5
x+4 + x= (x)(x+4)/1.5
both sides times 3
6x+12 = 2x(x+4)
2x^2 + 2x - 12 = 0
x^2 + x - 6 = 0
(x-2)(x+3) = 0
x = 2 or a negative, which would be silly
Dal would need 2 hours to do the job himself
To find out how long it will take Dal to assemble the swing set alone, we first need to determine the amount of work done per hour when both Dal and Kim work together.
Let's denote Dal's time to assemble the swing set alone as "x" hours. According to the information given, Kim takes 4 hours longer than Dal, so her time alone would be "x + 4" hours.
Now, let's calculate their individual rates of work. Dal's rate is 1/x (as he completes 1 swing set in x hours) and Kim's rate is 1/(x + 4) (since she completes 1 swing set in x + 4 hours).
When working together, their rates of work are additive, so their combined rate is 1/x + 1/(x + 4) swing sets per hour.
Given that they can assemble the swing set in 1.5 hours when working together, we can set up the equation:
1.5(1/x + 1/(x + 4)) = 1
Now, we solve for x:
1.5(x + 4 + x) = x(x + 4)
1.5(2x + 4) = x^2 + 4x
3x + 6 = x^2 + 4x
0 = x^2 + x - 6
Using the quadratic formula or factoring, we find that x = 2 or x = -3. However, as time cannot be negative, we disregard the negative solution.
Therefore, Dal would take 2 hours to assemble the swing set alone.