Question

A student rides on a bicycle at $8$ km/hour and reaches his school $2.5$ minutes late. The next day he increases the speed to $10$ km/hr and reaches school $5$ minutes early. How far is the school from the house?

• A. $6$ km
• B. $4$ km
• C. $5$ km
• D. $4.5$ km

Answer 1

Answer: (C)

$5$ km

Let the distance of his office be $x$km and thr right time to reach office be $t$ min

Time taken to reach office at $8$km/hr =$\frac{t+2.5}{60}=\frac{x}{8}$ (i)

Time taken to reach office at $10$km/hr =$\frac{x-5}{60}=\frac{x}{10}$ (ii)

Subtracting $\left(ii\right)$ from $\left(i\right)$ we get,

$\frac{7.5}{60}=\frac{x}{8}-\frac{x}{10}$

$\frac{7.5}{60}=\frac{5x-4x}{40}$

$x=\frac{7.5\times 40}{60}$

$x=5$km