Jordan is a manager of a car dealership. He has two professional car washers

Jordan is a manager of a car dealership. He has two professional car washers, Matthew and Arianna, to clean the entire lot of cars. Matthew can wash all the cars in 14 hours. Arianna can wash all the cars in 11 hours. Jordan wants to know how long it will take them to wash all the cars in the lot if they work together.

Write an equation and solve for the time it will take Matthew and Arianna to wash all the cars together. Explain each step.

4 Answers

  • If n denotes the total number of cars then

    Matthew washes n/14 cars per hour and

    Arianna washes n/11 per hour.

    Together they wash n/14+n/11=25n/154 per

    hour. The number of hour they take together

    is n/[25n/154] = 154/25 =6.16 hours

    =6 h 10 min approximately.

  • Mathew ALONE = 14 hours

    Mathew ALONE in 1 HOUR = 1/14 of the work

    Arianna ALONE in 1 HOUR = 1/11 of the work

    TOGETHER in 1 HOUR = 1/14+1/11 = 25/154 of the work

    TOGETHER they will FINISH THE WORK in 154/25 = 6.16 hours OR

    6 hours 9 minutes 36 seconds ANSWER

  • M does 1/14 job/hr

    A does 1/11 job/hr

    Together they do 1/14 + 1/11 job/hr

    t = 1 job /(1/14 + 1/11 job/hr)

    = 14(11)/(11+14)

    154/25 ~ 6 4/25 hours

    ~ 6 hrs 9 min 36 sec

    The key fact is their rates of doing work add.

  • if Arianna completes 1 job in 11 hours, she completes 1 / 11 of the job in one hour

    if Matthew completes 1 job in 14 hours, he completes 1 / 14 of the job in one hour

    let

    x = time it takes working together in hours

    m = matthew's time working alone in hours

    a = Arianna's time working alone in hours

    x[(1 / m) + (1 / a)] = 1 (job)

    x[(a + m) / am] = 1

    x(a + m) = am

    x = am / (a + m)

    x = (11 * 14) / (11 + 14)

    x = 154 / 25

    x = 6.16 hours

Leave a Reply

Your email address will not be published. Required fields are marked *

Related Posts