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

Question

Jordan manages a car dealership and employs two professional car washers, Matthew and Arianna, to clean the entire lot of cars. Matthew can wash all the cars in 14 hours, while Arianna can complete the task in 11 hours. Jordan is interested in determining how long it will take both of them to wash all the cars in the lot if they work together. Please write an equation to represent this scenario and solve for the total time it will take Matthew and Arianna to wash all the cars together. Additionally, provide a detailed explanation of each step involved in your solution.

Anonymous · Accepted Answer

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.

Anonymous · Answer

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

Jorge Koss · 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.

Anonymous · Answer

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

Anonymous

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

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