Lisa and alice leave alice's house at the same time. lisa drives north and alice drives west. lisa's average speed is 9 mph slower than alice's. at the end of one hour, they are 65 miles apart. find alice's average speed. (round your answer to the nearest tenth.)

The direction of movement of both are perpendicular to each other

Let us say Alice's speed = x mph

then speed of Lisa = x- 9 mph

The distance traveled by Lisa in 1 hour = 1 times ( x-9 ) = x-9 miles

the distance traveled by Alice in 1 hour = 1 times x = x miles

the distance between them is : the length of the hypotaneous of the triangle with perpendicular sides being x and x-9

That is : ( x^2 + ( x-9)^2 ) ^(1/2) which is given to be equal to 65

x^2 + ( x-9)^2 = ( 65)^2

x^2 + x^2 + 9^2 - 2* 9 x = 4225

2x ^2 - 18x = 4225 - 9^2

2x^2 - 18x = 4144

dividing each term by 2

x^2 - 9x = 2072

x^2 - 9x - 2072 = 0

we plug a= 1 b= -9 c=-2072 in the quadratic formula

x= [-b +/- ( b^2 - 4ac ) ]/ 2a

x= [ 9 +/- ( (-9)^2 - 4 ( 1)( -2072) ] / 2* 1

x= 50.24 miles /hour

Answer : Alice's average speed is 50.24 miles.

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