promotion image of download ymail app
Promoted
Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

math problem help?

A jogger ran 3 ​miles, decreased her speed by 1 mile per​ hour, and then ran another 4 miles. If her total jogging time was 2 and 1/12 hours, find her speed for each part of her run.

5 Answers

Relevance
  • 1 month ago

    LET THE SPEED BE X MPH FOR THE FIRST 3 MILES

    SPEED FOR THE NEXT 4 MILES = X-1   MPH

    TIME TAKEN =  3 /X + 4 / (X-1) = 25/12

    36( X-1) + 48X = 25X ( X-1)

    25X^2 - 109X  +36 = 0

    SOLVE  X = 9/25  OR 4

    X CANNOT BE 9/25

     X = 4

    ANSWER SPEEDS = 4MPH AND 3 MPH

    CHECK

    3/4 +4/3 = 9+16 /12 = 25/12 = 2 1/12 HOURS

    • Commenter avatarLogin to reply the answers
  • 2 months ago

    A jogger ran 3 ​miles, decreased her speed by 1 mile per​ hour, 

    and then ran another 4 miles. 

    If her total jogging time was 2 and 1/12 hours, 

    find her speed for each part of her run.

    let x = speed for 1st part of her run

    x - 1 = speed for 2nd part of her run

    travel time = distance/speed

    3/x + 4/(x - 1) = 25/12

    36/x + 48/(x - 1) = 25

    lcd = x(x - 1)

    36(x - 1) + 48x = 25x^2 - 25x 

    36x - 36 + 48x = 25x^2 - 25x

    25x^2 - 109x + 36 = 0

    (x - 4) (25 x - 9) = 0

    speed for 1st part of her run was 4 mph

    speed for 2nd part of her run  was 3 mph

    • Commenter avatarLogin to reply the answers
  • 2 months ago

    let s be speed in first leg

    then s–1 is speed in second leg

    t = d/s = 3/s + 4/(s–1) = 2 1/12 = 25/12

    3/s + 4/(s–1) = 25/12

    multiply by 12s(s–1)

    36(s–1) + 48s = 25s(s–1)

    36s – 36 + 48s = 25(s²–s)

    84s – 36 = 25s² – 25s

    25s² – 25s – 84s + 36 = 0

    25s² – 109s + 36 = 0

    using a solver, 

    s = 4 or 9/25 (second solution results in s–1 negative, rejectted_

    s–1 = 3 

    check 

    lap1, t = d/s = 3/4 = 0.75 hr

    lap2, t = 4/3 = 1.333 hr

    sum = 2.083 hr correct

    • Commenter avatarLogin to reply the answers
  • Bryce
    Lv 7
    2 months ago

    3/s + 4/(s - 1)= 25/12

    (3s - 3 + 4s)/(s² - s)= 25/12

    36s - 36 + 48s= 25s² - 25s

    25s² - 109s + 36= 0

    Solve by using the quadratic equation.

    s= 0.36, 4.  Use s= 4

    first speed= 4 mi/h, second speed= 3 mi/h

    • Commenter avatarLogin to reply the answers
  • How do you think about the answers? You can sign in to vote the answer.
  • 2 months ago

    Let s be the speed for the 3 mile portion.

    Let s -1 be the speed for the rest of the run.

    Total Time = 25/12 = Distance / Speed = (3 / s) + [4 / (s - 1)]

    25/12 = (3 / s) + [4 / (s - 1)]

    25 = (36 / s) + (48 / (s - 1))

    25(s)(s - 1) = 36(s - 1) + 48s

    25s^2 - 25s = 36s - 36 + 48s

    25s^2 - 25s = 84s - 36

    25s^2 - 109s + 36 = 0

    s = 4 mph, 9/25 mph.

    9/25 is an extraneous solution.

    So, the jogger ran 4 mph for the first part of the run and 3 mph for the second.

    • lauren2 months agoReport

      thank you!

    • Commenter avatarLogin to reply the answers
Still have questions? Get your answers by asking now.