# Question #91114

Dec 21, 2016

$12.5 k m$

#### Explanation:

Let distance from house be $d$
Let correct time be $t$. Converting given time in hours.

Time taken is found from the equation
$\text{Time"="Distance"/"Speed}$

1. When walking at $5 k m p h$
Let the person take time ${t}_{1} \text{ which is } t + \frac{10}{60} = \frac{d}{5}$
$\implies 60 t + 10 = 12 d$ .......(1)
2. In the second case, speed is increased by $1 k m p h$. Let the person take time ${t}_{2}$
${t}_{2} \text{ is } t - \frac{15}{60} = \frac{d}{6}$
$\implies 60 t - 15 = 10 d$ ......(2)

Subtracting equation (1) from (2) we get
$- 15 - 10 = 10 d - 12 d$
$\implies 2 d = 25$
$\implies d = 12.5 k m$