ted can clear a football field of debris in 3 hours. jacob can clear the same field in 2 hours. when they…

ted can clear a football field of debris in 3 hours. jacob can clear the same field in 2 hours. when they work together, the situation can be modeled by the equation, where (t) is the number of hours it would take to clear the field together. (\frac{1}{3}+\frac{1}{2}=\frac{1}{t}) how long will it take ted and jacob to clear the field together? 12 minutes 50 minutes 1 hour 12 minutes 2 hours 30 minutes

ted can clear a football field of debris in 3 hours. jacob can clear the same field in 2 hours. when they work together, the situation can be modeled by the equation, where (t) is the number of hours it would take to clear the field together. (\frac{1}{3}+\frac{1}{2}=\frac{1}{t}) how long will it take ted and jacob to clear the field together? 12 minutes 50 minutes 1 hour 12 minutes 2 hours 30 minutes

Answer

Explanation:

Step1: Find common denominator

First, find a common - denominator for the left - hand side of the equation $\frac{1}{3}+\frac{1}{2}=\frac{1}{t}$. The common denominator of 3 and 2 is 6. So, $\frac{1\times2}{3\times2}+\frac{1\times3}{2\times3}=\frac{1}{t}$, which simplifies to $\frac{2}{6}+\frac{3}{6}=\frac{1}{t}$, and further to $\frac{2 + 3}{6}=\frac{1}{t}$, or $\frac{5}{6}=\frac{1}{t}$.

Step2: Cross - multiply

Cross - multiply the equation $\frac{5}{6}=\frac{1}{t}$ to get $5t=6$.

Step3: Solve for t

Divide both sides of the equation $5t = 6$ by 5. So, $t=\frac{6}{5}$ hours.

Step4: Convert to minutes

Since 1 hour = 60 minutes, $\frac{6}{5}$ hours is $\frac{6}{5}\times60 = 72$ minutes, which is 1 hour 12 minutes.

Answer:

1 hour 12 minutes