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Quadratic Equations

A journey of 300km would take 2 hours less if the speed was increased by 5kmph. Find the original speed.


Distance covered =d=300km

Let original speed = skmph

Then, original time =t1=ds=300s hours

New speed =s+5kmph

New time = t_2 = \dfrac{300}{s + 5} \; hours

As per sum, \; t_2 = t_1 - 2

i.e. \; \dfrac{300}{s + 5} = \dfrac{300}{s} - 2

i.e. \; \dfrac{150}{s + 5} = \dfrac{150}{s} - 1

i.e. \; 150 s = 150 s + 750 - s \left(s + 5\right)

i.e. \; s^2 + 5 s - 750 = 0

i.e. \; s^2 + 30 s - 25 s - 750 = 0

i.e. \; s \left(s + 30\right) - 25 \left(s + 30\right) = 0

i.e. \; \left(s + 30\right) \left(s - 25\right)= 0

i.e. \; s = -30 \; or \; s = 25

\because \; Original speed cannot be negative, original speed = 25 \; kmph