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