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geniusboy [140]
3 years ago
10

John and Paul both run on the same track each morning. The ratio of the number of miles John runs to the number of miles Paul ru

ns is 5:8.
Mathematics
1 answer:
nirvana33 [79]3 years ago
4 0

Answer:

Step-by-step explanation:

For example,

<u>Solution: Finding a unit rate</u>

If we divide 150 by 20, we get the unit rate for the ratio, 150 minutes for every 20 miles.

150÷20=7.5

So the runner is running 7.5 minutes per mile. We can multiply this unit rate by the number of miles:

7.5 minutes mile × 6 miles = 45 minutes

Thus it will take her 45 minutes to run 6 miles at this pace.

If it takes her 45 minutes to run 6 miles, it will take her 45÷3=15 minutes to run 6÷3=2 miles at the same pace.

If it takes her 15 minutes to run 2 miles, it will take her 4×15=60 minutes to run 4×2=8 miles at the same pace. Since 60 minutes is 1 hour, she is running at a speed of 8 miles per hour.

We found her pace in minutes per miles in part (a).

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Read 2 more answers
How do you solve for x in this quadratic equation?: 5x^2 – 34x + 24 = 0
wlad13 [49]
Quadratic formula
factoring
graphing 
completing the square
factoring by grouping
Rational Roots Theorem
synthetic division

Take a look at <span>5x^2 – 34x + 24 = 0.  The last term could have been the result of these different possible muliplications:  1*24, 2*12, 3*8, 4*6.  The leading term is 5, whose factors are 5 and 1.  Thus, possible rational roots would be
4/5 (the 4 is a factor of 24 and the 5 is a factor of 5) and 6/1 (the 6 is a factor of 24 and the 1 is a factor of 5).  

Using synth. div. to check whether 6 is actually a root:
     ___________________
6  /    5      -34          24
                  30         -24
    ------ --------------------------
         5       -4             0

since the remainder is 0, we can safely call 6 a "root."  
Note the remaining coefficients, 5 and -4:  

They correspond to the factor 5x - 4.  If we set this difference = to 0, and solve for x, we get  x = 4/5 (which is correct).

The roots of </span><span>5x^2 – 34x + 24 = 0  are  x = 4/5 and x= 6/1.</span>
5 0
4 years ago
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