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

Algebra ->  Customizable Word Problem Solvers  -> Travel -> 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      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

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) About Me  (Show Source):
You can put this solution on YOUR website!
              rate       time            distance
part1          r        10%2Fr              10
part2         r+10      25%2F%28r%2B10%29          25
Total                   3%2F4

Answer by addingup(3677) About Me  (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