Solve (2pi/365-2pi/687)T=2pi

$$( \frac { 2 \pi } { 365 } - \frac { 2 \pi } { 687 } ) T = 2 \pi$$

Solve for T

$$T = \frac{250755}{322} = 778\frac{239}{322} \approx 778.742236025$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 250755, the least common multiple of 365,687.

$$250755\left(\frac{2\pi }{365}-\frac{2\pi }{687}\right)T=501510\pi$$

Combine \frac{2\pi }{365} and -\frac{2\pi }{687} to get \frac{322}{250755}\times 2\pi .

$$250755\times \frac{322}{250755}\times 2\pi T=501510\pi$$

Express \frac{322}{250755}\times 2 as a single fraction.

$$250755\times \frac{322\times 2}{250755}\pi T=501510\pi$$

Multiply 322 and 2 to get 644.

$$250755\times \frac{644}{250755}\pi T=501510\pi$$

Cancel out 250755 and 250755.

$$644\pi T=501510\pi$$

Cancel out \pi on both sides.

$$644T=501510$$

Divide both sides by 644.

$$T=\frac{501510}{644}$$

Reduce the fraction \frac{501510}{644} to lowest terms by extracting and canceling out 2.

$$T=\frac{250755}{322}$$