Answer
After $4$ hours, the buses will be $400$ miles apart.
Work Step by Step
Bus $A$ travels with a speed of $55$ miles per hour. Therefore, after $x$ hours, it will have traveled $55x$ miles. On the other hand, Bus $B$ travels with a speed of $45$ miles per hour. Therefore, after $x$ hours, it will have traveled $45x$ miles.
To find the number of hours, after which the distance between the buses will be $400$ miles, we set up the following equation.
$55x +45x = 400$
To solve the equation for $x$, first, we combine the like terms.
$100x = 400$
Then, we divide both sides of the equation by $100$.
$\dfrac{100x}{100} = \dfrac{400}{100}\\
x = 4$
Thus, after $4$ hours, the buses will be $400$ miles apart.
