Answer:
(A)56
Explanation:
The distance covered by Chuck = 112 miles
The distance covered by Dana = 106 miles
Let Dana's rate of travel = x miles per hour
Chuck's rate of travel is 3 miles per hour more than Dana's, therefore:
Chuck's rate of travel = (x+3) miles per hour
Rate = Distance/Time
For Chuck
[tex]\begin{gathered} x+3=\frac{112}{t} \\ t(x+3)=112 \\ t=\frac{112}{x+3} \end{gathered}[/tex]For Dana
[tex]\begin{gathered} x=\frac{106}{t} \\ xt=106 \\ t=\frac{106}{x} \end{gathered}[/tex]Since they travel the same length of time
[tex]\begin{gathered} \frac{112}{x+3}=\frac{106}{x} \\ \text{Cross multiply} \\ 112x=106(x+3) \\ 112x=106x+318 \\ 112x-106x=318 \\ 6x=318 \\ x=\frac{318}{6} \\ x=53 \end{gathered}[/tex]Since Chuck's speed = (x+3) miles per hour
Chuck's speed = 53+3
=56 miles per hour.
