Question

Represent the following situation in the form of the quadratic equation:
A train travels a distance of $480km$ at a uniform speed. If the speed had been $8km/h$ less, then it would have taken $3$ hours more to cover the same distance. We need to find the speed of train.

Answer 1

Let's say speed of train is $s\left(km/H\right)$ and time $t\left(inHours\right)$ is taken to reach the distance $d.$

Given that: $d=480km$

According to first condition,

$\frac{d}{t}=s$

$ts=480$ ......(1)

According to second condition,

$(t+3)(s-8)=480$ ......(2)

From equation(1) and (2),

$ts=st-24+3s-8t$

$8t=(3s-24)$

Substituting in equation (1),

$8ts=8\times 480$,

$(3s-24)s=3840$,

$3(s^2-8s)=3840$,

$(s^2-8s)=1280$,

$s^2-8s-1280=0$,

$s^2-(40-32)s-1280=0$

$s^2-40s+32s-1280=0$

$s(s-40)+32(s-40)=0$

$(s+32)(s-40)=0$

Since speed can not be negative,

Hence, $s-40=0ors=40km/H$

The initial speed of the train is $40km/H.$