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iragen [17]
3 years ago
15

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

ur longer than Tamara to go 80 miles, how fast can Samantha ride her bike?
Mathematics
1 answer:
Triss [41]3 years ago
6 0

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

<u>Time taken by Samantha</u>

=\frac{80}{x}

<u>Time taken by Tamara</u>

=\frac{80}{4+x}

<u>Equation for difference in time</u>

=\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

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The equivalent ratio is 8 : 4.

And the missing values are as follows 21, 6 and 48.

Complete table be,

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Given, a ratio table

Plum     14   42   __   __

Grape    7    __    3    24

we have to find the missing values and the equivalent ratios.

in the first ratio,

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Now, in the second ratio,

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x = 21

Now, in the third ratio,

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Now, in the forth ratio,

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So, the equivalent ratio is 8 : 4.

And the missing values are as follows 21, 6 and 48.

Hence, the equivalent ratio is 8 : 4.

And the missing values are as follows 21, 6 and 48.

Complete table be,

Plum     14   42   6   48

Grape    7    21    3    24

Learn more about Ratios and Proportions here brainly.com/question/26974513

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Step-by-step explanation:

Given

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Required:

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When the equation is translated 7 units right, this implies a negative unit along the x axis.

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The expression can be further simplified but it's best left in the form of

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