Question

If I walk at the rate of $5$ km/hr, I will be late by $7$ minutes, but if I walk at the rate of $6$ km/hr I will be early by $5$ minutes. The distance to be covered in km is

• A. $60$
• B. $12$
• C. $10$
• D. $6$

Answer 1

The correct option is D $6$

Let the required time be $t$ and distance $d$

For speed $5km/h=5\times \frac{1000}{60}=83.33m/min$

$d=\mathrm{83.33.}(t+7)-\left(1\right)$

For speed $6km/h=6\times \frac{1000}{60}=100m/min$

$d=100.(t-5)-\left(2\right)$

On solving eqs.$\left(1\right)$ and $\left(2\right)$

$83.33(t+7)=100(t-5)$

$83.33t+583.31=100t-500$

$83.33t-100t=-500-583.31$

$-16.67t=-1083.31$

$t=\frac{-1083.31}{-16.67}$

we get, $t=63.58min$

Then distance $d=100(63.58-5)=100.\left(58.58\right)=5858m=5.85km=6km\left(approx\right)$