First Principles AI

Accedmychevron_right11thchevron_rightmathchevron_rightTheory Of Quadratic Functionschevron_rightExercise 3.2

Solution

Let the original speed be $v$ km/h.

Time at original speed:

\frac{48}{v}

If speed is $v-2$ , time is:

\frac{48}{v-2}

Given the slower speed takes 2 hours more:

\frac{48}{v-2}-\frac{48}{v}=2

Multiply by $v(v-2)$ :

48v-48(v-2)=2v(v-2)

96=2v^2-4v

Divide by 2:

v^2-2v-48=0

(v-8)(v+6)=0

So $v=8$ (reject $v=-6$ ).

Time taken:

\frac{48}{8}=6

\boxed{\text{He took 6 hours.}}