Question

Arjun travelled $240$ miles at a certain speed. If he were to increase his speed by $20mph$, it would have taken him $2$ hours less to travel same distance. What was his speed in mph?

• A. 30
• B. 40
• C. 50
• D. 60
• E. 80

Answer 1

The correct option is B 40

Distance $d=240miles$

Let his initial speed be $v$ and time taken be $t$

So, $240=vt$

$⟹t=\frac{240}{v}$

Now new speed $v^{\prime }=v+20$

New time $t^{\prime }=t-2$

So, $240=v^{\prime }{t}^{\prime }=(v+20)(t-2)$

Or $240=vt-2v+20t-40$ ($vt=240$)

Or $v-10t+20=0$

Or $v-10\times \frac{240}{v}+20=0$

Or $v^2+20v-2400=0$

$⟹v=40mph$