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.
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)
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
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