Difficult proportional examples
6 workers can build 4 bikes in 2 days. How many days would it take 8 workers to build 6 bikes?
Using the rules of inversely proportional it is easy to work out how long it would take 8 workers to build 4 bikes.
`6wo\rkers\times2\ days=8wo\rkers\timesx\ days`
Simplifying we get
So it takes `1\1/2` days for 8 workers to build 4 bikes.
To build 6 bikes would therefore take `1\1/2` this time
Therefore `1\1/2times1\1/2\ \days=3/2times3/2=9/4\ \days`
Tracey completes a task in 2 hours. Brenda completes the same task in 3 hours. How long would it take Tracy and Brenda to complete the task together?
To answer this try and find the work rate per hour for each person. This would then provide you with the work rate per hour together.
Tracy is `1/2` task per hour
Brenda is `1/3` task per hour
Together Tracy `+` Brenda per hour `=1/2` task `+1/3` task
So in one hour together they can complete `5/6`ths of the task.
Using our maths section on percentages we can find.
`x=1` task done
Put the divide sign in
re-arranging to put `x` on its own
`x=1`hours and `1/5`of an hour
or `x=1`hour `12` minutes
`x` is directly proportional to `y^2` when `x=4` and `y=6`
What is the value of `y` when `x=8`?
Using our knowledge on ratios
and then using our knowledge on direct proportions
rearranging the formula to get `y` on its own.