Question

a chemical storage tank is to be filled by three pipes. the first two transmit 930 L/h of liquid each and the third transmits 560 L/h. if the third pipe starts working 90 minutes after the first two begin and the tank has a capacity of 4000 L, how long (in hours) will it take after the first two pipes begin working to fill the tank?

Answer 1

we have two different rates

first period: 2x 930L/h
= 1860 L/h

second period: 1860 L/h + 560 L/h
= 2420 L/h

Answer 2

also, we know the first period lasted 90m
which is 1,5 hours

tank so far: 1,5 x 1860 = 2790 L

Answer 3

tell me if everything is clear so far

Answer 4

yes I understand

Answer 5

theres an error

Answer 6

where?

Answer 7

I should not have divided by the time it takes, but multiplied

Answer 8

we are still 4000L - 2790 L = 1210 L from the tank being filled

the remaining 1210 L are filled at the second rate of 2420 L/h

the time it takes:
\[1210L = \frac{ 2420 L }{ 1h } \times x h\]

Answer 9

if we input at 2420L/h for one hour, we get 2420L

if we input at 2420L/h for half an our, we get... 1210 L

Answer 10

the equation is satisfied with "additional hours": x = 0.5
\[1210L = \frac{ 2420 L \times 0.5 h}{ 1h } =\frac{ 1210 L }{ 1 }\]

Answer 11

so 1210 L

Answer 12

wait i need hours though ...how do i find that?

Answer 13

"how long (in hours) will it take after the first two pipes begin working to fill the tank?"

it will take 90 m + 30 m to fill the tank

Answer 14

oh ok

Answer 15

because the x value we have chosen is 0.5

that is half an hour additional to 90m already passed

Answer 16

go it

Answer 17

in total it takes 1.5 + 0.5 = 2 hours

Answer 18

thanks