Container 𝑋 and container 𝑌 are emptied. The table shows information about all of the water flowing out of the two containers. Complete the table.
Container 𝑋 had an average flow rate of 2100 centimetres cubed per hour. And the total amount of water was 700 centimetres cubed. Container 𝑌 had an average flow rate of 945 centimetres cubed per hour and took one hour, 45 minutes to empty. The units for average flow rate are centimetres cubed per hour. Centimetres cubed is a measure of volume. And hours are a measure of time. As the units are per hour, the average flow rate is calculated by dividing the amount of water in centimetres cubed by the time taken in hours. Let’s firstly consider container 𝑋 where we need to calculate the time taken.
If we let the time taken be letter 𝑡, then substituting our values into the formula gives us 2100 equals 700 divided by 𝑡 as the average flow rate was 2100 centimetres cubed per hour. And the amount of water was 700 centimetres cubed. To solve this equation, we can firstly multiply both sides by 𝑡. This gives us 2100𝑡 is equal to 700. We can then calculate the value of 𝑡 by dividing both sides by 2100.
On the left-hand side, 2100 divided by 2100 is one. So we’re just left with 𝑡. On the right-hand side, we’re left with 700 over or divided by 2100. We can simplify this fraction by dividing the numerator and denominator by 100. This leaves us with seven over 21. Seven and 21 are both divisible by seven. Seven divided by seven is equal to one. And 21 divided by seven is equal to three. This means that the time taken to empty container 𝑋 is one-third of an hour. One hour is equal to 60 minutes. To calculate the number of minutes in a third of an hour, we need to divide 60 minutes by three. This is equal to 20 minutes. Therefore, the time taken for container 𝑋 to empty was 20 minutes.
Let’s now consider the missing value for container 𝑌. This is the amount of water that was in the container. As our units for the average flow rate were in centimetres cubed per hour, we firstly need to change the time into just hours. One hour and 45 minutes is equal to 1.75 hours. This is because 45 minutes is three-quarters of an hour. And three-quarters as a decimal is 0.75. If we let the amount of water in container 𝑌 be letter 𝑤, substituting our numbers into the formula gives us 945 is equal to 𝑤 divided by 1.75. The average flow rate was 945 centimetres cubed per hour. And the time taken was 1.75 hours.
Multiplying both sides of this equation by 1.75 gives us 𝑤 is equal to 1.75 multiplied by 945. Typing this into our calculator gives us an answer of 1653.75. This means that the amount of water initially in container 𝑌 was 1653.75 centimetres cubed. Whilst it was not needed for this question, it is worth remembering that one centimetre cubed is equal to one millilitre. It is possible that the amount of water could’ve been given in millilitres instead of centimetres cubed.
The two missing answers in the table were 20 minutes and 1653.75 centimetres cubed.