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A is twice efficient than B. A and B can both work together to complete a work in 7 days. Then find in how many days, A alone can complete the work?
Correct answer is '10.5'. Can you explain this answer?
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A is twice efficient than B. A and B can both work together to complet...
**Understanding the Problem:**
Let's assume that A can complete the work in x days, and B can complete the work in y days.
Given information:
- A is twice as efficient as B.
- A and B together can complete the work in 7 days.
**Formulating Equations:**
From the given information, we can derive the following equations:
1. A is twice as efficient as B:
A's efficiency = 2 * B's efficiency
A's efficiency = 1/x (assuming A completes the work in x days)
B's efficiency = 1/y (assuming B completes the work in y days)
2. A and B together can complete the work in 7 days:
A's daily work = 1/x
B's daily work = 1/y
(A's daily work) + (B's daily work) = 1/7
**Solving the Equations:**
To solve the equations, we need to eliminate one variable to find the value of the other variable.
From equation 1, we know that A's efficiency is twice as much as B's efficiency. So, we can rewrite equation 2 as:
(2/x) + (1/y) = 1/7
Multiplying both sides of the equation by 14xy, we get:
14y + 14x = 2xy
Rearranging the equation, we obtain:
2xy - 14x - 14y = 0
Applying the quadratic formula, we can solve for x:
x = [14 ± √(14² - 4 * 2 * (-14))] / (2 * 2)
Simplifying further:
x = [14 ± √(196 + 112)] / 4
x = [14 ± √308] / 4
Since the time taken to complete the work cannot be negative, we take the positive value:
x = (14 + √308) / 4
Calculating the value of x:
x ≈ 10.5
Therefore, A alone can complete the work in approximately 10.5 days.
Let's assume that A can complete the work in x days, and B can complete the work in y days.
Given information:
- A is twice as efficient as B.
- A and B together can complete the work in 7 days.
**Formulating Equations:**
From the given information, we can derive the following equations:
1. A is twice as efficient as B:
A's efficiency = 2 * B's efficiency
A's efficiency = 1/x (assuming A completes the work in x days)
B's efficiency = 1/y (assuming B completes the work in y days)
2. A and B together can complete the work in 7 days:
A's daily work = 1/x
B's daily work = 1/y
(A's daily work) + (B's daily work) = 1/7
**Solving the Equations:**
To solve the equations, we need to eliminate one variable to find the value of the other variable.
From equation 1, we know that A's efficiency is twice as much as B's efficiency. So, we can rewrite equation 2 as:
(2/x) + (1/y) = 1/7
Multiplying both sides of the equation by 14xy, we get:
14y + 14x = 2xy
Rearranging the equation, we obtain:
2xy - 14x - 14y = 0
Applying the quadratic formula, we can solve for x:
x = [14 ± √(14² - 4 * 2 * (-14))] / (2 * 2)
Simplifying further:
x = [14 ± √(196 + 112)] / 4
x = [14 ± √308] / 4
Since the time taken to complete the work cannot be negative, we take the positive value:
x = (14 + √308) / 4
Calculating the value of x:
x ≈ 10.5
Therefore, A alone can complete the work in approximately 10.5 days.
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A is twice efficient than B. A and B can both work together to complete a work in 7 days. Then find in how many days, A alone can complete the work?Correct answer is '10.5'. Can you explain this answer?
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