[tex]{\large{\boxed{\mathfrak{Question}}[/tex]
A plane's average speed when flying from one city to another is 550 mi/h and is 430 mi/h on the return flight. To the nearest mile per hour, what is the plane's average speed for the entire trip?
[tex]{\large{\boxed{\mathfrak{Formula}}}[/tex]
The formula to find the average speed is distance divided by time
[tex]{\large{\boxed{\mathfrak{Equation\:to\:find\:average\:speed}}}[/tex]
Let a be the average speed
[tex]\frac{1}{550}+\frac{1}{430} =\frac{2}{a}[/tex]
Since we don't want our denominator's we will get rid of them by multiplying the [tex]LCM[/tex] between the two numbers.
Definition of LCM - The smallest quantity that is divisible by two or more given quantities, also known as Least Common Multiple
Multiply both sides by [tex]23650a[/tex] since that is our LCM.
Now our equation is
[tex]43a+55a=47300[/tex]
[tex]{\underline{simplify}}[/tex]
[tex]98a=47300[/tex]
Since we want to isolate the average speed on one side or also known as [tex]a[/tex] we will divide both sides by 98
[tex]a=482.653[/tex] miles per hour
[tex]{\large{\boxed{\mathfrak{Answer}}}[/tex]
Our average speed is [tex]482.653[/tex] miles per hour or [tex]483[/tex] miles per hour
