Answer: (15/2, 33/2) or (7.5, 16.5)
depending on if you want fractions or decimals

explanation:
equation for midpoint... (avg x, avg y)
x-coordinate: (6+9)/2 = 15/2 = 7.5
y-coordinate: (17+16)/2 = 33/2 = 16.5

4 0

3 years ago

Two sisters like to compete on their bike rides. Tamara can go 4 mph faster than her sister, Samantha. If it takes Samantha 1 ho

Triss [41]

Answer:

16 mph

Step-by-step explanation:

You should first form equations related to this information

Given,Tamara can go 4 mph faster than her sister, Samantha

Lets take speed to ride a bike for Samantha to be= x mph

The speed to ride a bike for Tamara will be= x+4 mph

To cover a distance of 80 miles, Samantha takes 1 hour longer than Tamara

Introduce the formula for time; time=distance/speed=D/S where D is distance in miles and S is speed in miles per hour

Here time Samantha takes to cover a distance of 80 miles is 1 hour more than that taken by Tamara, hence

Time taken by Samantha

$=\frac{80}{x}$

Time taken by Tamara

$=\frac{80}{4+x}$

Equation for difference in time

$=\frac{80}{x} -\frac{80}{4+x} =1$

Solve the equation for difference in time to get value of x which is samantha speed

$=\frac{80}{x} -\frac{80}{x+4} =1\\\\\\=80(4+x)-80(x)=x(4+x)\\\\\\=320+80x-80x=4x+x^2\\\\\\=x^2+4x-320=0$

Solve quadratic equation by the quadratic formula where a=1,b=4 and c=-320

x=(-b±√b²-4ac)÷2a

x=(-4±√4²-4×1×-320)÷2×1

$x=\frac{-4+/-\sqrt{4^2-4*1*-320} }{2} \\\\\\x=(-4+/-\sqrt{1296} )/2\\\\\\x=\frac{-4+36}{2} =\frac{32}{2} =16$

Samantha speed is 16 mph

6 0

3 years ago