Question

An aeroplane covers a distance of 1500km in a certain time at a certain speed.After increasing the speed by 100km/hr, it covers the same distance in a time which is half an hour less than the previous time. Find the previous speed of the aeroplane.

this is from quadratic equations CBSE grade 10
please answer ASAP

Answer 1

previous speed of the aeroplane is 500 km/hr

Explanation:

Given: Distance covered by aeroplane = 1500 km

It covers the same distance in a time which is half an hour less than the previous time if the speed is increased by 100 km/hr

To find: previous speed of the aeroplane

Solution:

Let x denotes the previous speed of the aeroplane.

Time taken by an aeroplane if speed is x km/hr = distance/speed =
`(1500)/(x)` hours

If speed is increased by 100 km/hr, new speed = (x + 100) km/hr

Time taken by an aeroplane if speed is (x + 100) km/hr =
`(1500)/(x+100)` hours

According to question,

`(1500)/(x+100)=(1500)/(x)-(1)/(2)\\ (1500)/(x)-(1500)/(x+100)=(1)/(2) \\(1)/(x)-(1)/(x+100)=(1)/(3000)\\ (x+100-x)/(x(x+100))=(1)/(3000)\\ x^2+100x=300000\\x^2+100x-300000=0\\`

`x^2+600x-500x-300000=0\\x(x+600)-500(x+600)=0\\(x-500)(x+600)=0\\x=500\,,\,-600`

As speed can not be negative,
`x=-600` is rejected.

So,

previous speed of the aeroplane is 500 km/hr