Question

A plane left 30 minutes late than its schedule time and in order to reach the destination 1500 km away in time it had to increase its speed by 100km/hr from the usual speed find its usual speed (class 10th)

Answer 1

Let x= the usual speed
1500/x would equal how long it usually took the plane to read the destination
1500/(x+100) would equal how long it would take the plane now
So
`(1500)/(x) - (1500)/(x+100) = (1)/(2)` because it would lose 30 minutes already
Simplify:

`(1500(x+100)-1500x)/(x(x+100)) = (1)/(2)`

`(1500x+150000-1500x)/(x^2+100x) = (1)/(2)`

`(150000)/(x^2+100x) = (1)/(2)`

`(300000)/(x^2+100x) =1`

`300000= x^(2) +100x x^2+100x-300000=0 x^2+600x-500x-300000=0 x(x+600)-500(x+600) (x-500)(x+600) x=500, x \\eq -600`

The usual speed was 500 hm/hr