Respuesta :
Answer:
34 mph.
Step-by-step explanation:
Let x be speed of Charlene, then speed of Paul will be x+16 as we are given that Paul is driving 16 mph faster than Charlene.
Let y be distance covered by Charlene, then distance covered by Paul will be 420-y.
Now we will use formula [tex]\text{Speed}=\frac{\text{Distance}}{\text{Time}}[/tex]. Upon using our given information we will get two equation and two unknowns as:
[tex]x+16=\frac{420-y}{5}...(1)[/tex]
[tex]x=\frac{y}{5}...(2)[/tex]
Upon substituting [tex]x=\frac{y}{5}[/tex] in 1st equation we will get,
[tex]\frac{y}{5}+16=\frac{420-y}{5}[/tex]
Upon multiplying both sides of our equation by 5 we will get,
[tex]5(\frac{y}{5}+16)=420-y[/tex]
[tex]5\times\frac{y}{5}+5\times 16=420-y[/tex]
[tex]y+80=420-y[/tex]
[tex]y+80+y=420-y+y[/tex]
[tex]2y+80=420[/tex]
[tex]2y=420-80[/tex]
[tex]2y=340[/tex]
[tex]y=\frac{340}{2}[/tex]
[tex]y=170[/tex]
Upon substituting y=170 in 2nd equation we will get,
[tex]x=\frac{170}{5}[/tex]
[tex]x=34[/tex]
Therefore, Charlene's speed is 34 miles per hour.
