Question

If I had walked 1km/h faster, I would've taken 10 minutes less to walk 2km. Find the rate of my walking.

Answer 1

Distance travelled = 2 km
Let the original speed be x km/hr
Time taken $=\frac{distance}{speed}$
$T_1=\frac{2}{x}\dots \dots \left(i\right)$
Now, speed increased by 1 km/hr
Now time taken $\left(T_2\right)=\frac{2}{x+1}\dots \dots \left(ii\right)$
$T_1-T_2=10min=\frac{10}{60}min$
$=\frac{1}{6}hr$
So, $\frac{1}{6}=\frac{2}{x}-\frac{2}{x+1}$
$\frac{1}{12}=\frac{1}{x}-\frac{1}{x+1}$
$\frac{1}{12}=\frac{x+1-x}{x(x+1)}$
$x(x+1)=12$
$x^2+x-12=0$
$x^2+4x-3x-12=0$
$x(x+4)-3(x+4)=0$
$x=-4,x=3$
Speed can't be negative
So speed = 3 km/hr.