Respuesta :
We are given that Haley travels 223 miles, first at a speed of 16 mph and then at a speed of 53 mph if x is the number of hours driving at 16 mph and y the number of hours traveling at 53 mph, this can be expressed mathematically as:
[tex]16x+53y=223,(1)[/tex]We are also told that the total number of hours is 7, this can be represented as:
[tex]x+y=7,(2)[/tex]We get a system of two variables and two equations. To solve the system we will solve for "x" in equation (2) by subtracting "y" to both sides:
[tex]x=7-y[/tex]Replacing the value of "x" in equation (1):
[tex]16(7-y)+53y=223[/tex]Using the distributive property:
[tex]112-16y+53y=223[/tex]Adding like terms:
[tex]112+37y=223[/tex]Subtracting 112 to both sides:
[tex]\begin{gathered} 37y=223-112 \\ 37y=111 \end{gathered}[/tex]Dividing by 37 both sides:
[tex]y=\frac{111}{37}[/tex]Solving the operations:
[tex]y=3[/tex]Replacing the value of "y" in equation (2)
[tex]x=7-3=4[/tex]Therefore, she traveled 4 hours at 16 mph and 3 hours at 53 mph
