WEBVTT
00:00:01.520 --> 00:00:04.520
Container π and container π are emptied.
00:00:05.280 --> 00:00:10.440
The table shows information about all of the water flowing out of the two containers.
00:00:11.200 --> 00:00:12.040
Complete the table.
00:00:14.000 --> 00:00:20.440
Container π had an average flow rate of 2100 centimetres cubed per hour.
00:00:21.080 --> 00:00:25.080
And the total amount of water was 700 centimetres cubed.
00:00:26.680 --> 00:00:40.120
Container π had an average flow rate of 945 centimetres cubed per hour and took one hour, 45 minutes to empty.
00:00:40.120 --> 00:00:44.560
The units for average flow rate are centimetres cubed per hour.
00:00:45.400 --> 00:00:48.880
Centimetres cubed is a measure of volume.
00:00:48.880 --> 00:00:50.520
And hours are a measure of time.
00:00:52.400 --> 00:01:03.280
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.
00:01:04.800 --> 00:01:09.880
Letβs firstly consider container π where we need to calculate the time taken.
00:01:11.360 --> 00:01:28.440
If we let the time taken be letter π‘, then substituting our values into the formula gives us 2100 equals 700 divided by π‘ as the average flow rate was 2100 centimetres cubed per hour.
00:01:29.000 --> 00:01:32.600
And the amount of water was 700 centimetres cubed.
00:01:34.360 --> 00:01:38.720
To solve this equation, we can firstly multiply both sides by π‘.
00:01:40.000 --> 00:01:44.320
This gives us 2100π‘ is equal to 700.
00:01:45.760 --> 00:01:51.560
We can then calculate the value of π‘ by dividing both sides by 2100.
00:01:53.200 --> 00:01:58.560
On the left-hand side, 2100 divided by 2100 is one.
00:01:59.160 --> 00:02:00.480
So weβre just left with π‘.
00:02:02.040 --> 00:02:08.640
On the right-hand side, weβre left with 700 over or divided by 2100.
00:02:10.520 --> 00:02:16.120
We can simplify this fraction by dividing the numerator and denominator by 100.
00:02:16.680 --> 00:02:19.240
This leaves us with seven over 21.
00:02:21.120 --> 00:02:23.960
Seven and 21 are both divisible by seven.
00:02:24.680 --> 00:02:26.960
Seven divided by seven is equal to one.
00:02:27.440 --> 00:02:30.480
And 21 divided by seven is equal to three.
00:02:32.400 --> 00:02:38.200
This means that the time taken to empty container π is one-third of an hour.
00:02:39.960 --> 00:02:42.240
One hour is equal to 60 minutes.
00:02:43.400 --> 00:02:49.120
To calculate the number of minutes in a third of an hour, we need to divide 60 minutes by three.
00:02:50.840 --> 00:02:53.040
This is equal to 20 minutes.
00:02:54.400 --> 00:02:59.720
Therefore, the time taken for container π to empty was 20 minutes.
00:03:01.480 --> 00:03:04.720
Letβs now consider the missing value for container π.
00:03:05.400 --> 00:03:08.240
This is the amount of water that was in the container.
00:03:10.040 --> 00:03:18.920
As our units for the average flow rate were in centimetres cubed per hour, we firstly need to change the time into just hours.
00:03:20.200 --> 00:03:25.320
One hour and 45 minutes is equal to 1.75 hours.
00:03:26.720 --> 00:03:30.280
This is because 45 minutes is three-quarters of an hour.
00:03:30.920 --> 00:03:34.800
And three-quarters as a decimal is 0.75.
00:03:37.160 --> 00:03:50.760
If we let the amount of water in container π be letter π€, substituting our numbers into the formula gives us 945 is equal to π€ divided by 1.75.
00:03:52.320 --> 00:03:57.280
The average flow rate was 945 centimetres cubed per hour.
00:03:57.880 --> 00:04:01.600
And the time taken was 1.75 hours.
00:04:03.120 --> 00:04:13.960
Multiplying both sides of this equation by 1.75 gives us π€ is equal to 1.75 multiplied by 945.
00:04:15.480 --> 00:04:22.840
Typing this into our calculator gives us an answer of 1653.75.
00:04:24.480 --> 00:04:34.600
This means that the amount of water initially in container π was 1653.75 centimetres cubed.
00:04:36.760 --> 00:04:44.560
Whilst it was not needed for this question, it is worth remembering that one centimetre cubed is equal to one millilitre.
00:04:45.320 --> 00:04:51.840
It is possible that the amount of water couldβve been given in millilitres instead of centimetres cubed.
00:04:54.720 --> 00:05:03.960
The two missing answers in the table were 20 minutes and 1653.75 centimetres cubed.