Question

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, how far into the country does he go?

Answer 1

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

$Time =\frac{Distance}{Speed}$

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

$\frac{x}{10} +\frac{x}{3} = 6.5$

L.C.M of (10,3) = 30

Than the equation becomes

3x +10x = 195

solving

13x = 195

$x = \frac{195}{13}$

x = 15 miles into the country

Hence proved