Is my solution for the tank word problem correct?

In summary, the larger pipe can fill a tank in 40 minutes, the smaller pipe can fill it in 50 minutes while the drain is open, and the time required for the drain to empty the tank is 22.83 minutes when the pipes are closed. However, the given solution is incorrect and needs to be revised.
  • #1
paulmdrdo1
385
0
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?
 
Last edited:
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  • #2
paulmdrdo said:
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.

paulmdrdo said:
$1800x+1440x=74000$
After multiplying by $72000x$, the right-hand side is $2000x$, not just $2000$, so this equation is wrong.
 

FAQ: Is my solution for the tank word problem correct?

What is a "filling a tank" word problem?

A "filling a tank" word problem is a type of mathematical problem that involves determining how long it will take to fill a tank with a certain amount of liquid, given the rate at which the liquid is being added.

What is the formula for solving a "filling a tank" word problem?

The formula for solving a "filling a tank" word problem is: Time = Volume / Rate

How do I determine the rate at which the tank is being filled?

The rate at which the tank is being filled can be determined by dividing the volume of liquid added by the time it took to add that volume. For example, if 100 liters of water were added in 5 minutes, the rate would be 100 liters / 5 minutes = 20 liters per minute.

What units should I use when solving a "filling a tank" word problem?

When solving a "filling a tank" word problem, it is important to use consistent units for both volume and time. For example, if the volume is given in liters, the time should be given in minutes or hours. It is also important to use the same units when using the formula: Time = Volume / Rate.

What should I do if the tank is being filled at a variable rate?

If the tank is being filled at a variable rate, the best approach is to divide the problem into smaller segments and solve for each segment separately. For example, if the tank is being filled at 10 liters per minute for the first 5 minutes, then at 15 liters per minute for the next 10 minutes, you would calculate the volume filled in the first 5 minutes and add it to the volume filled in the next 10 minutes to determine the total volume and time.

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