Let usual speed of aeroplane be x km/hr. Given, distance =1200 km
Time taken for journey of 1200 km `=(1200)/(x) "hours"" "(because "Time"="Distance"/"Speed")`
When the speed is increased by 100 km/hr, time taken for same journey `=(1200)/(x+100)` hours.
According to given condition
`(1200)/(x)-(1200)/(x+100)=1`
`implies(1200(x+100)-1200x)/(x(x+100))=1`
`implies1200x+120000-1200x=x^(2)+100x`
`impliesx^(2)+100x-120000=0`
`impliesx^(2)+400x-300x-120000=0`
`impliesx(x+400)-300(x+400)=0`
`implies(x+400)(x-300)=0`
`impliesx=-400orx=300`
`impliesx=300km//hr" ("because "speed cannot be negative")`
The usual speed = 300km/hr.
