|
Question 48949: A reservoir has two drain systems, large & small. Six large drains, on their own, can drain the reservoir in 12 hours. Three large pipes and 9 small pipes can drain it in 8 hours. How long will it take 5 small pipes to drain the reservoir.
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! more important is your statement that it is for 6 th.grade
test and your mention on algebra.if it is for 6 th. grade ,they may
not be exposed to algebra that much and hence my answer is of no use
,if it is not ubderstood by the student.so let me give you below a
method which needs only general maths principles.
Question 48949: A reservoir has two drain systems, large & small. Six
large drains, on their own, can drain the reservoir in 12 hours. Three
large pipes and 9 small pipes can drain it in 8 hours. How long will
it take 5 small pipes to drain the reservoir.
: A reservoir has two drain systems, large & small. Six large drains,
on their own, can drain the reservoir in 12 hours. Three large pipes
and 9 small pipes can drain it in 8 hours. How long will it take 5
small pipes to drain the reservoir.
6..................... large drains....... can drain in ...........12
hours.....................1 reservoir
6........................
l.d.....................................................1.h..............................1/12
r
1.........................l.d.....................................................1.h.................1/(12*6)=1/72
r
-----------------------------------------------------------------------------------------------------------------
3 l + 9 s........................................................................8
h.........................1 r
3 l + 9 s.........................................................................1............................1/8
r
but from above 1 large can drain in 1 hr 1/72 r...hence 3 l can drain
in 1 hr..3/72=1/24 r
hence 9 s can drain in 1 hr ....1/8 - 1/24 =2/24=1/12 r.
9 s..................................................................................1............................1/12
r
1 s..................................................................................1.............................1/108
r
----------------------------------------------------------------------------------------------------------------------
from above 5 s will drain
5s................................................................................1....................5*1/108=5/108
r
5 s will need .................................................................108/5
hrs.............1 r
answer =21.6 hrs.
hope this will be clear to your child.
----------------------------------------------------------------------------
A reservoir has two drain systems, large & small. Six large drains, on their own, can drain the reservoir in 12 hours. Three large pipes and 9 small pipes can drain it in 8 hours. How long will it take 5 small pipes to drain the reservoir.
LET EACH LARGE DRAIN CAPACITY =L
LET EACH SMALL DRAIN CAPACITY=S
SIX LARGE HAS=6L CAP.
LET RESERVOIR VOLUME =R
TIME TAKEN TO DRAIN WITH 6 LARGE=R/6L=12 HRS................
L=R/72..................I
3 LARGE HAS =3L CAP.
9 SMALL HAS =9S CAP.
TOTAL DRAIN CAP.=3L+9S=3(L+3S)
TIME TAKEN TO DRAIN=R/3(L+3S)=8......................
L+3S=R/24
3S=(R/24)-(R/72)=2R/72=R/36
S=R/108
5 SMALL CAP.=5S=5R/108
HENCE TIME NEEDED TO DRAIN =R/(5R/108)=108/5=21.6 HRS
|
|
|
| |
