A Train travelled a certain distance at a uniform speed. If the train had been 7 km/hr faster, it would have taken 14 hours less than the scheduled time. If the train were slower by 3 km/hr then it would have taken 10 hours more than the scheduled time. Find the distance covered by the train.
600 Km
700 Km
800 Km
900 Km
Explanation:
$\frac{d}{x}-\frac{d}{x+7}=14---->(1)$
$\frac{d}{x-3}-\frac{d}{x}=10----->(2)$
$\frac{ d[x+7-x]}{x(x+7)}=14 $
$7d=14x(x+7)$
$d=2x(x+7)------>(3)$
$\frac{d[x-(x-3)]}{x(x-3)]}=10$
$3d=10x(x-3)$
$d=\frac{10}{3}x(x-3)----->(4)$
$From (3) & (4)$
$2x(x+7)=\dfrac{10}{3}x(x-3)$
$2x+21=5x-15$
$2x=36$
$x=18kmph$
$(1)----->\dfrac{d}{18}-\dfrac{d}{25}=14$
$\dfrac{25d-18d}{450}$
$=14$
$d=900km$