Question

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.)

Answer 1

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.