Answer
Find out the how far into the country does he go.
To proof
Let us assume that the total diatance travelled into the country be x .
Formula
[tex]Time =\frac{Distance}{Speed}[/tex]
As given
A cyclist rides into the country at an average speed of 10 miles per hour. When his bicycle gets a flat tire,
he walks it back at an average speed of 3 miles per hour.
If he returns home 6 and a half hours after he starts i.e the total time including the bike time and walk time of the cyclist be 6.5 hours.
Than the equation becomes
[tex]\frac{x}{10} +\frac{x}{3} = 6.5[/tex]
L.C.M of (10,3) = 30
Than the equation becomes
3x +10x = 195
solving
13x = 195
[tex]x = \frac{195}{13}[/tex]
x = 15 miles into the country
Hence proved
