SOLUTION: father and a his son can dig a well if the father works 6 hours and his son works 12 hours or they can do its if the father works 9 hours and the son works 8 hours. How long will

Algebra ->  Rate-of-work-word-problems -> SOLUTION: father and a his son can dig a well if the father works 6 hours and his son works 12 hours or they can do its if the father works 9 hours and the son works 8 hours. How long will       Log On


   

Question 745794: father and a his son can dig a well if the father works 6 hours and his son works 12 hours or they can do its if the father works 9 hours and the son works 8 hours. How long will it take for the son to dig the well alone?
Found 3 solutions by josmiceli, stanbon, josgarithmetic:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You can add their rates of digging to get their rate
working together
Let +R%5B1%5D+ = father's rate of digging
Let +R%5B2%5D+ = Son's rate of digging
--------------------------------
In general, I can say that:
( time spent digging ) x ( rate of digging ) = fraction of job done
---------------
given:
(1) +6R%5B1%5D+%2B+12R%5B2%5D+=+1+
(2) +9R%5B1%5D+%2B+8R%5B2%5D+=+1+
( note that +1+ means entire job done )
----------------
Multiply both sides of (1) by +3+ and
both sides of (2) by +2+
Then subtract (2) from (1)
----------------------
(1) +18R%5B1%5D+%2B+36R%5B2%5D+=+3+
(2) +-18R%5B1%5D+-+16R%5B2%5D+=+-2++
+20R%5B2%5D+=+1+
+R%5B2%5D+=+1%2F20+
-----------------
(1) +6R%5B1%5D+%2B+12R%5B2%5D+=+1+
(1) +R%5B1%5D+%2B+2R%5B2%5D+=+1%2F6+
(1) +R%5B1%5D+%2B+2R%5B2%5D+=+1%2F6+
(1) +R%5B1%5D+%2B+2%2A%281%2F20%29+=+1%2F6+
(1) +R%5B1%5D+=+1%2F6+-+1%2F10+
(1) +R%5B1%5D+=+5%2F30+-+3%2F30+
(1) +R%5B1%5D+=+2%2F30+
(1) +R%5B1%5D+=+1%2F15+
-----------------
The son would take 20 hrs working alone
check:
(2) +9R%5B1%5D+%2B+8R%5B2%5D+=+1+
(2) +9%2A%281%2F15%29+%2B+8%2A%281%2F20%29+=+1+
(2) +9%2F15+%2B+8%2F20+=+1+
(2) +36%2F60+%2B+24%2F60+=+60%2F60+
(2) +1+=+1+
OK







Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
father and a his son can dig a well if the father works 6 hours and his son works 12 hours or they can do its if the father works 9 hours and the son works 8 hours. How long will it take for the son to dig the well alone?
----
Let "f" be the father's rate and "s" the son's rate.
Equations:
6f + 12s = 1 job
9f + 8s = 1 job
---------------------------
Multiply top equation by 9
Multiply bottom equation by 6
------
54f + 108s = 9
54f + 48s = 6
----
Subtract and solve for "s"
60s = 3
s = 1/20 job/hr
son's time = 20 hrs/job
-----------------------------
Cheers,
Stan H.

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x = father's rate
y = son's rate
Those rates are in jobs/hour
1 job is digging the well.
These two ways will complete 1 job:
x%2A6%2By%2A12
and
x%2A9%2By%2A8

They each equal 1 job, so we have
x%2A6%2By%2A12=1
and
x%2A9%2By%2A8=1
Two equations with two unknown variables to solve.

Suggestion is multiply the first by 3, multiply the second by 2, and subtract one resulting equation from the other resulting equation. Here is the initial part:
18x%2B36y=3+
and
18x%2B16y=2
and you do first minus second and obtain 20y=1, so highlight%28y=1%2F20%29, and ....

(Looks like the son does 1 job in 20 hours, or works for 20 hours to do the job alone, himself.)