To find the value of \(x\), let's first understand the formula for power. Power (\(P\)) is defined as the work done (\(W\)) over time (\(t\)):
P = \(\frac{W}{t}\)
According to the problem, person 'A' completes 500 J of work in \(x\) minutes, and person 'B' does 1000 J of work in 20 minutes.
Given that the power delivered by 'A', \(P_1\), is twice the power delivered by 'B', \(P_2\):
\(P_1 = 2P_2\)
Now calculate the power delivered by each:
- For 'A':
- For 'B':
Simplifying \(P_2\):
\(P_2 = \frac{1000}{1200} = \frac{5}{6} \, \text{W}\)
Substitute the expression for \(P_2\) into the equation \(P_1 = 2P_2\):
\(\frac{500}{x \times 60} = 2 \times \frac{5}{6}\)
Solving the equation:
\(\frac{500}{x \times 60} = \frac{10}{6}\)
Cross-multiply to solve for \(x\):
\(500 \times 6 = 10 \times x \times 60\)
3000 = 600x
\(x = \frac{3000}{600} = 5\)
Therefore, the value of \(x\) is 5 minutes.
Hence, the correct answer is: 5
