<span>Answer:
Roma Sherry drove 330 miles from her hometown to Tucson. During her return trip, she was able to increase her speed by 11 mph. If her return trip took 1 hour less time, find her original speed and her speed returning home.
:
Let s = original speed
then
(s+11) = return speed
:
Write a time equation: Time = distance%2Fspeed
:
Original time = return time + 1 hr
330%2Fs = 330%2F%28%28s%2B11%29%29 + 1
:
Multiply equation by s(s+11) and you have:
330(s+11) = 330s + s(s+11)
:
330s + 3630 = 330s + s^2 + 11s
:
0 = 330s - 330s + s^2 + 11s - 3630
:
A quadratic equation:
s^2 + 11s - 3630 = 0
Factor this to:
(s + 66)(s - 55) = 0
Positive solution
s = 55 mph is original speed.
:
Find the time
330/55 = 6 hr, original time
and
330/66 = 5 hrs, faster time; confirms our solution.</span>
Answer: 47/8
Step-by-step explanation: To write a mixed number as an improper fraction, first multiply the denominator by the whole number and then add the numerator. Finally, we will put our new number over our old denominator and we have our answer which is 47/8.
Therefore, 
can be rewritten as the improper fraction 47/8.
First, set up the equation.
365x + 125 = 250x + 175
Second, combine like terms on the same side by subtracting 250x and 125 from both sides.
365x +125 = 250x + 175
-250x -125 -250x -125
__________________
115x = 50
Third, divide both sides by 115 to solve for x.
115x = 50
---- ----
115 115
Fourth, simplify.
x=50/115=10/23 or 0.435
When finding the reciprocal, it is basicaly flipping the numerator and denominator of the number. For instance, the reciporcal of 2 is 1/2, because the denominator of 2 would be 1. For an example more straight forward, the reciporacle of 3/5 is 5/3. This applied to the question goes as followed.
1. 3/5 is 5/3
2. 1/4 is 4
3. 1 is 1
Similarly when dividing fractions or an integer to a fraction, the fraction that is dividing the number turns into the reciprocal then you would multiply.
4. 3/(3/4) is 3*4/3= 4
5. 5/(3/4) is 5*(4/3)= 20/3
6. 8/(4/7) is 8*(7/3)= 56/3
7. 6/(3/5) is 6*(5/3)= 10
8. 2/(5/8) is 2*(8/5)= 16/5
9. 4/(8/9) is 4*(9/8)= 9/2
