The bailey family is traveling 565.5 miles for a family vacation. if
they estimate they can travel 78 miles per hour, then how many hours
will take for the baileys to arrive?

7.25 hours (or 7 hr 15 minutes)

Step-by-step explanation:

Lets use the distance equation to solve this problem. This is very easy...

Distance Equation

D = RT

Where

D is the distance (in miles)

R is the rate (in mi/hr)

T is the time (in hours)

Given in the problem:

Distance = D = 565.5 miles

Rate = R = 78 miles per hour

We want T, the time in hours it will take to drive. So we substitute the known parameters into the formula and  solve for T:

So, it is going to take around 7.25 hours for them to arrive.

The extra 0.25 hours means:

0.25 Hours * 60 Minutes/Hour = 15 minutes

Or, we can say it will take 7 hours and 15 minutes for them to arrive.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240