Respuesta :
Answer:
[tex]\frac{48}{r+9}=\frac{12}{r}[/tex]
Step-by-step explanation:
Let r represent Linda's walking rate.
We have been given that Linda can ride 9 mph faster than she can walk, so Linda's bike riding rate would be [tex]t+9[/tex] miles per hour.
[tex]\text{Time}=\frac{\text{Distance}}{\text{Rate}}[/tex]
We have been given that Linda can bicycle 48 miles in the same time as it takes her to walk 12 miles.
[tex]\text{Time while riding}=\frac{48}{r+9}[/tex]
[tex]\text{Time taken while walking}=\frac{12}{r}[/tex]
Since both times are equal, so we will get:
[tex]\frac{48}{r+9}=\frac{12}{r}[/tex]
Therefore, the equation [tex]\frac{48}{r+9}=\frac{12}{r}[/tex] can be used to solve the rates for given problem.
Cross multiply:
[tex]48r=12r+108[/tex]
[tex]48r-12r=12r-12r+108[/tex]
[tex]36r=108[/tex]
[tex]\frac{36r}{36}=\frac{108}{36}[/tex]
[tex]r=3[/tex]
Therefore, Linda's walking at a rate of 3 miles per hour.
Linda's bike riding rate would be [tex]t+9\Rightarrow 3+9=12[/tex] miles per hour.
Therefore, Linda's riding the bike at a rate of 12 miles per hour.
