SOLUTION: solution to work problem ramon cna do the weekly billing in 2 hrs luann needs three hours. if roman works for 30 minute and then is joined by luann, how long will it take them t

Question 187863This question is from textbook algebra structure and methoed
: solution to work problem
ramon cna do the weekly billing in 2 hrs luann needs three hours. if roman works for 30 minute and then is joined by luann, how long will it take them to finish
the tens digit of a two digit number is one more than 3 times the unit digit.
subtracting 45 from the number reverses it , find the original number
This question is from textbook algebra structure and methoed

Found 2 solutions by ankor@dixie-net.com, solver91311:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Ramon can do the weekly billing in 2 hrs; Luann needs three hours. If Romon
works for 30 minutes, and then is joined by Luann, how long will it take them
to finish?
:
Let t = amt of time required for them to finish
:
Change 30 min to .5 hrs
:
Let the completed job = 1
:
+ = 1
Multiply equation by 6 to get rid of denominators, results:
3(t+.5) + 2t = 6
:
3t + 1.5 + 2t = 6
:
5t = 6 - 1.5
:
5t = 4.5
t =
t = .9 hrs which is .9(60) = 54 min to finish the job
;
Check solution:
+ =
+ =
.7 + .3 = 1
:
:
the tens digit of a two digit number is one more than 3 times the unit digit.
:
Let x = the 10's digit, and let y = units
then
10x + y = the two digit number
:
Write an equation for the statement:
"the tens digit of a two digit number is one more than 3 times the unit digit."
x = 3y + 1
:
subtracting 45 from the number reverses it ,
10x + y - 45 = 10y + x
10x - x = 10y - y + 45
9x = 9y + 45
Simplify, divide equation by 9
x = y + 5
:
find the original number
:
Substitute (3y+1) for x in the above equation
3y + 1 = y + 5
3y - y = 5 - 1
2y = 4
y = 2
then
x = 2 + 5
x = 7
:
72 is our number
;
;
Check solution in the statement:"subtracting 45 from the number reverses it"
72 - 45 = 27
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

If Ramon worked for 30 minutes (1/2 hour) on a job that takes 2 hours, he would have completed 1/4 of the job, leaving 3/4 of the job remaining which would take him 3/2 hours to complete by himself. If Luann needs 3 hours to do the whole job, then it would take her 3 times 3/4 = 9/4 hours to do the remainder of the job.

If Ramon can do the rest of the job in 3/2 hours, then he can do 2/3 of the job in one hour. Likewise, Luann can do 4/9 of the job in one hour. Together, they can do:

of the job in one hour, therefore, it will take them

of an hour

to complete the remainder of the job, and

minutes.

******************************************
Let x be the tens digit and y be the units digit. We are given that:

Also, the number must be:

And the number reversed must be:

And we are given that:

Substituting:

So the units digit is 2 and the tens digit is 3(2) + 1 = 7. And the number is then 72.

Answer checks.
John

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