algebra

posted by .

A jogger ran 6 miles, decreased her speed by 1 mile per hour and than ran another 7 miles. If total jogging time was 2 1/42, find speed for each part of her run.

  • algebra -

    first speed --- x
    second speed --- x-1
    time at first speed = 6/x
    time at 2nd speed = 7/(x-1)

    6/x + 7/(x-1) = 2 1/42 = 85/42
    times: 42x(x-1)
    6(42)(x-1) + 7(42)x = 85x(x-1)
    252x - 252 + 294x = 85x^2 - 85x
    85x^2 - 631x + 252 = 0
    x = (631 ± √312481)/170
    = 7 or ...
    aha , it facored
    (x-7)(85x - 36) = 0
    x=7 or x = 36/85
    but 36/85 would make his 2nd speed negative, not very likeyly, so
    x = 7

    for the first leg he ran at 7 mph, for the 2nd leg he ran at 6 mph

    check: 6/7 + 7/6 = (36+49)/42 = 85/42 = 2 1/42

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Algebra (check answers)

    Could you please check my answers we are using substitution to solve each system of equations. And at the end of every solution you are supposed to have an answer as a coordinate. 1. x=2y x+y=3 Answer (1,2) 2. 2y=3 x-y=10 Answer: (10,10) …
  2. PSAT - Math

    Hello, I am reviewing my psat and looking at the questions I got wrong. I can't understand how to do this problem. Mike and paul left their houses at the same time for a fitness run to the park. Mike ran at an average speed of 7 miles …
  3. algebra

    Rachel allows herself 1 hour to reach a sale appointment 50 mile s away. After she has driven 30 miles, she realizes that she must increase her speed by 15 miles per hour in order to get there on time. What was her speed for the first …
  4. algebra

    A jogger leaves home and runs at a constant speed of 4 miles per hour. Nine minutes later, a bicyclist follows along the same route at a constant speed of 15 miles per hour. Find the bicyclist's travel time needed to catch the jogger.
  5. Math

    Leroy ran a total of 15 miles last month. He ran 5/8 mile each day. How many days did he run?
  6. math

    A marathon runner ran 26.2 miles in 2 h 30 min. Find these rates: a. miles per hour b. miles per minute c. minutes per mile
  7. math

    Jan Maya and Sara ran a total of 64 miles. two ran the same and one ran 8 less. how many miles did they run?
  8. algebra

    monique ran one mile in 6 minutes.her average speed was how many miles per hour
  9. algebra

    A student runs 100 meters in 11 seconds. What is the speed of the student?
  10. math

    Ava and Kelly ran a road race, starting from the same place at the same time. Ava ran at an average speed of 6 miles per hour. Kelly ran at an average speed of 8 miles per hour.

More Similar Questions