Question

An aircraft pilot flies it at a distance of $800km$ with some average speed. He could have saved $40$ minutes by increasing the average speed of the aircraft by $40km/h$. Find actual speed of the aircraft.

Answer 1

$d=800km$

Say average speed is $v$ and time taken is $t$ then

$vt=800$ ......(1)

According to given condition, he could have saved $40$ minutes if speed increased by $40km/h$

$(v+40)(t-\frac{2}{3})=800$

$(v+40)(3t-2)=3\times 800$

Or

$3vt+120t-2v-80=3vt$ [from equation (1)]

$60t-v-40=0$

$\frac{60\times 800}{v}-v-40=0$

$v^2+40v-48000=0$

$v^2+240v-200v-48000=0$

$(v+240)(v-200)=0$

Hence,

$v=200km/hor-240km/h\left(notconsiderable\right)$

So, actual speed of the aircraft is $200km/h.$