MHB Is my solution for the tank word problem correct?

[paulmdrdo1]

please check my work here

1. The larger of the two pipes can fill a tank in 40 min. and the smaller can fill it in 50 min. while the drain is opened. Find the time required for the drain to empty the full tank if the pipes are closed.

Solution

$\frac{1}{40}+\frac{1}{50}-\frac{1}{x}=\frac{1}{36}$---> multiply this by 72000x

$1800x+1440x=74000$

$3240x=74000$

where $x=$ the time required for the drain to empty the tank

solving for x I get $x=22.83\text{min}$

is my answer correct?

 

[Evgeny.Makarov]

1. The larger of the two pipes can fill a tank in 40 min. and the smaller can fill it in 50 min. while the drain is opened. Find the time required for the drain to empty the full tank if the pipes are closed.

Solution

$\frac{1}{40}+\frac{1}{50}-\frac{1}{x}=\frac{1}{36}$---> multiply this by 72000x

Did you forget to write another condition that has to do with 36 minutes? Next, why multiply by 72000 when the LCM(40, 50, 36) = 1800? At most 7200 will do.

$1800x+1440x=74000$

After multiplying by $72000x$, the right-hand side is $2000x$, not just $2000$, so this equation is wrong.