SOLUTION: uniform motion. a woman drives 10 miles, then increases her speed by 10 miles per hour and drives another 25 miles. find the original speed if she drove for 45 minutes

Question 1009506: uniform motion. a woman drives 10 miles, then increases her speed by 10 miles per hour and drives another 25 miles. find the original speed if she drove for 45 minutes
Found 2 solutions by josgarithmetic, addingup:
Answer by josgarithmetic(39615) (Show Source): You can put this solution on YOUR website!

rate time distance part1 r 10 part2 r+10 25 Total

Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
Let the original speed be x. Then, time it took to travel the first 10 miles
= 10/x
Then we increase the speed
= (x+10) and since the distance at this speed is 25
= 25/(x+10)
Finally, the above is 10mph. But she only drove for 45 minutes. We can't have apples and oranges. We need to convert the 45 minutes to hours
= 45/60= 0.75 hour
---------------------------------------
total time:
= (10/x)+(25/(x+10))= 0.75 Put the fractions over a common denominator:
= {(10(x+10))/(x(x+10)}+{25x/(x(x+10))}= 0.75 Combine into a single fraction:
= (10(x+10)+25x)/(x(x+10))= 0.75Simplify. Distribute 10 over x+10:
= (10x+100+25x)/(x(x+10))= 0.75 Add x on top:
= (35x+100(/(x(x+10))= 0.75 Rewrite 0.75 as a fraction. 0.75= 3/4:
= (35x+100(/(x(x+10))= 3/4 Cross multiply so we get rid of fractions:
= 4(35x+100)= 3(x(x+10) Multiply on both sides to get rid of parentheses. Remember to multiply from the inside out, so on the right first x*x and x*10 and then 3*x^2 and 3*10x:
= 140x+400= 3x^2+30x Let's set the equation to 0:
= 140x+400-3x^2+30x = 0 Factor the left side (FOIL):
= -((x-40)(3x+10))= 0 Multiply times -1:
= (x-40)(3x+10)= 0 Split into 2 equations:
x-40= 0 or 3x+10= 0
x= 40 or 3x= -10 The answer we are getting on the right is negative, we are looking for a positive number. Our answer is on the left:
Answer: x= 40 is the original speed
J
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