Dal and Kim can assemble a swing set in 1/1/2 hrs,working alone it takes Kim 4 hrs longer than Dal to assemble the swing set.How long would it take Dal to working alone to assemble the set
Dal takes d
Kim takes k
Dal&Kim take b (for both)
1/b = 1/d + 1/k
1/(3/2) = 1/d + 1/(d+4)
2/3 = 1/d + 1/(d+4)
multiply through by 3d(d+4) to get
2d(d+4) = 3(d+4) + 3d
2d^2 + 8d = 3d + 12 + 3d
2d^2 + 2d - 12 = 0
d^2 + d - 6 = 0
(d+3)(d-2) = 0
d = -3 or 2
must have positive time, so d=2
That is, Dal takes 2 hours by himself
check:
1/2 + 1/6 = 2/3 = 1/(3/2)
To find out how long it would take Dal to assemble the swing set alone, we need to use the given information. Let's break it down step by step:
1. We know that Dal and Kim together can assemble the swing set in 1/1/2 hours. To simplify the fraction, we convert 1 1/2 hours to an improper fraction: 3/2 hours.
2. We also know that if Kim works alone, it takes her 4 hours longer than Dal to assemble the swing set. Let's denote the time it takes Dal to assemble the swing set alone as "D" hours. Therefore, it would take Kim D + 4 hours to assemble the swing set alone.
3. Now, we can create an equation based on the given information. The equation is: 1/3 + 1/(D + 4) = 1/2
- The left side of the equation represents the combined work rate of Dal and Kim.
- The right side of the equation represents the work rate needed to assemble the swing set in 1/2 hours.
4. To solve the equation, we can multiply both sides by the least common multiple (LCM) of the denominators, which is 6. Multiplying throughout the equation gives us:
2 + 6/(D + 4) = 3
5. Let's simplify the equation:
Multiply (D + 4) to both sides:
2(D + 4) + 6 = 3(D + 4)
Distribute and simplify:
2D + 8 + 6 = 3D + 12
Combine like terms:
2D + 14 = 3D + 12
6. To isolate the variable D, subtract 3D from both sides:
2D - 3D + 14 = 3D - 3D + 12
Simplify:
-D + 14 = 12
7. Now, subtract 14 from both sides:
-D + 14 - 14 = 12 - 14
Simplify:
-D = -2
8. Finally, divide both sides by -1 to solve for D:
-D/(-1) = -2/(-1)
Simplify:
D = 2
The value of D, which represents the time it takes Dal to assemble the swing set alone, is 2 hours.
Therefore, it would take Dal 2 hours to assemble the swing set alone.