a tank of dimensions 70cm x 40cm x 25cm if half filled. Tap A takes 5 minutes to fill the remaining part whereas Tap B removes the water in the tank at the rate of 10.5 litres/minute. find the time taken to fill 3/10 of the volume of water in the tank when both taps are kept on?

Asked by Āß | 18th Mar, 2017, 09:36: AM

Expert Answer:

begin mathsize 12px style straight A space tank space of space dimensions space 70 space cm space straight x space 40 space cm space straight x space 25 space cm space if space half space filled. space
rightwards double arrow Volume space of space half space of space the space tank space equals 70000 space equals 70 space litres space left parenthesis Since space 1 space litres equals 1000 space cm cubed right parenthesis
Volume space of space half space of space the space tank space equals 70 space litres
Tap space straight A space takes space 5 space minutes space to space fill space the space remaining space part comma space that space is comma space half space of space the space tank.
So comma space the space rate space at space which space tap space straight A space fills space half space of space the space tank space equals space 70 over 5 equals 14 space litres divided by min
Given space that space Tap space straight B space removes space the space water space in space the space tank space at space the space rate space of space 10.5 space litres divided by minute.
3 over 10 left parenthesis Volume space of space the space tank right parenthesis equals 3 over 10 left parenthesis 70 cross times 2 right parenthesis equals 42 space litres
Let space the space time space taken space to space fill space 42 space litres space be space straight t space mins
So comma space 14 straight t minus 10.5 straight t equals 42
rightwards double arrow 3.5 straight t equals 42
rightwards double arrow straight t equals fraction numerator 42 over denominator 3.5 end fraction
rightwards double arrow straight t equals fraction numerator 42 cross times 10 over denominator 35 end fraction
rightwards double arrow straight t equals 12 space mins
So comma space the space time space taken space to space fill space 3 over 10 space of space the space tank space is space 12 space mins. end style

Answered by Rebecca Fernandes | 18th Mar, 2017, 07:26: PM