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

Question

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.

Dr. Summer Schneider PhD · Accepted Answer

If n denotes the total number of cars thenMatthew washes n/14 cars per hour and Arianna washes n/11 per hour.Together they wash n/14+n/11=25n/154 perhour. The number of hour they take together is n/[25n/154] = 154/25 =6.16 hours =6 h 10 min approximately.

Dr. Summer Schneider PhD · Answer

Mathew ALONE = 14 hoursMathew ALONE in 1 HOUR = 1/14 of the workArianna ALONE in 1 HOUR = 1/11 of the workTOGETHER in 1 HOUR = 1/14+1/11 = 25/154 of the workTOGETHER they will FINISH THE WORK in 154/25 = 6.16 hours OR 6 hours 9 minutes 36 seconds ANSWER

Dr. Summer Schneider PhD · Answer

M does 1/14 job/hrA does 1/11 job/hrTogether they do 1/14 + 1/11 job/hrt = 1 job /(1/14 + 1/11 job/hr)= 14(11)/(11+14)154/25 ~ 6 4/25 hours~ 6 hrs 9 min 36 secThe key fact is their rates of doing work add.

Dr. Summer Schneider PhD · Answer

if Arianna completes 1 job in 11 hours, she completes 1 / 11 of the job in one hourif Matthew completes 1 job in 14 hours, he completes 1 / 14 of the job in one hourletx = time it takes working together in hoursm = matthew's time working alone in hoursa = Arianna's time working alone in hoursx[(1 / m) + (1 / a)] = 1 (job)x[(a + m) / am] = 1x(a + m) = amx = am / (a + m)x = (11 * 14) / (11 + 14) x = 154 / 25x = 6.16 hours

Dillan Pacocha

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

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