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Jack walked up a hill at a speed of $(x^2-11x-22)$ miles per hour. Meanwhile, Jill walked a total distance of $(x^2-3x-54)$ miles in $(x 6)$ hours. If Jack and Jill walked at the same speed, what is that speed, in miles per hour

Respuesta :

MrRoyal

Jack and Jills' speed in miles per hour is 4

How to determine the speed in miles per hour?

The given parameters are:

Jack speed = x^2-11x-22

Jill distance = x^2-3x-54 and time = x + 6

Speed is calculated as:

Speed = Distance/time

So, we have:

Jill speed = x^2-3x-54/x + 6

Factorize the numerator

Jill speed = (x + 6)(x - 9)/x + 6

Cancel the common factor

Jill speed = x - 9

Both speeds are equal.

So, we have:

x^2-11x-22 = x - 9

Collect like terms

x^2-11x - x -22 + 9 = 0

Evaluate

x^2 - 12x - 13 = 0

Factorize the expression

(x + 1)(x - 13) = 0

Solve for x

x = -1 or x = 13

x cannot be negative.

So, we have:

x =13

Substitute x =13 in Jill speed = x - 9

Jill speed = 13 - 9

Evaluate

Jill speed = 4

Hence, their speed in miles per hour is 4

Read more about speed at:

https://brainly.com/question/4931057

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