A police cruiser, approaching a right-angled intersection from the north, is chasing a speeding car that has turned the corner and is now moving straight cast. When the cruiser is `0.6` mile north of the intersection and the car is `0.8` mile to the east, the police determine with radar that the distance between them and the car is increasing at 20 mph. If the cruiser is moving at 60 mph at the instant of measurement, what is the speed of the car ?

Explanation

`s=sqrt(x^(2)+y^(2))`
` rArr " " s^(2)= x^(2) + y^(2) `
`rArr " " 2s(ds)/(dt)=2x(dx)/(dt)+2y(dy)/(dt)`
`rArr " " 2xx1xx20=2xx(8)/(10)xx(dx)/(dt)+2 xx(6)/(10)xx-60`
`rArr " " (8)/(5) (dx)/(dt) =40 + 72 +112`
`(dx)/(dt)=(112 xx5)/(8) =70 "mile"//hr`