Answer :
We are given that a person can bicycle 26 miles in the same time it takes to walk 6 miles. If we say that "x" is the walking speed in mph then since he can ride 10 mph faster than we can walk we have the following relationship:
[tex]\frac{26}{x+10}=\frac{6}{x}[/tex]this relationship comes from the fact that the velocity is defined as the distance over time, like this:
[tex]v=\frac{d}{t}[/tex]Since we are given that times are equal, then if we solve for the time we get:
[tex]t=\frac{d}{v}[/tex]Therefore, the distance over the velocity gives us the time and since the times are equal, we get the relationship. Now we can solve for "x" by cross multiplying:
[tex]26x=6(x+10)[/tex]Now we apply the distributive property on the right side:
[tex]26x=6x+60[/tex]Now we subtract 6x from both sides:
[tex]\begin{gathered} 26x-6x=6x-6x+60 \\ 20x=60 \end{gathered}[/tex]Now we divide both sides by 20:
[tex]\begin{gathered} \frac{20x}{20}=\frac{60}{20} \\ x=3 \end{gathered}[/tex]Therefore, the walking speed is 3 mph. Now we need to determine the time it takes to walk 35 miles. We do that applying the formula for the time we got previously:
[tex]t=\frac{d}{v}[/tex]Plugging in the values we get:
[tex]t=\frac{35}{3}=11.7[/tex]therefore, the time is 11.7 hours.
