Brad can mow a lawn in 75 min. The next week Capri mows the same lawn in 60 min. How long would it take them to mow the lawn working together?
Make this chart:
| Number of | Rate | Time
| lawns | in | to
| mowed | lawns/min | complete
-----------------------|-------------|-----------|----------
Brad mowing alone | | |
-----------------------|-------------|-----------|----------
Capri mowing alone | | |
-----------------------|-------------|-----------|----------
Both mowing together | | |
------------------------------------------------------------
How long would it take them to mow the lawn working together?
Let x = the answer and put x in the middle of the last column, the
time for them to mow 1 lawn working together. So we put x in the
bottom right corner
| Number of | Rate | Time
| lawns | in | to
| mowed | lawns/min | complete
-----------------------|-------------|-----------|----------
Brad mowing alone | | |
-----------------------|-------------|-----------|----------
Capri mowing alone | | |
-----------------------|-------------|-----------|----------
Both mowing together | | | x
------------------------------------------------------------
Brad can mow a lawn in 75 min.
So put 75 in the top of the last column, or the time required for Brad
to mow 1 lawn.
| Number of | Rate | Time
| lawns | in | to
| mowed | lawns/min | complete
-----------------------|-------------|-----------|----------
Brad mowing alone | | | 75
-----------------------|-------------|-----------|----------
Capri mowing alone | | |
-----------------------|-------------|-----------|----------
Both mowing together | | | x
------------------------------------------------------------
Capri mows the same lawn in 60 min.
So put 60 in the middle right column, the time required when Capri mows
alone:
| Number of | Rate | Time
| lawns | in | to
| mowed | lawns/min | complete
-----------------------|-------------|-----------|----------
Brad mowing alone | | | 75
-----------------------|-------------|-----------|----------
Capri mowing alone | | | 60
-----------------------|-------------|-----------|----------
Both mowing together | | | x
------------------------------------------------------------
In all three cases exactly 1 lawn was mowed, so we put 1's in all three
spaces in the first column:
| Number of | Rate | Time
| lawns | in | to
| mowed | lawns/min | complete
-----------------------|-------------|-----------|----------
Brad mowing alone | 1 | | 75
-----------------------|-------------|-----------|----------
Capri mowing alone | 1 | | 60
-----------------------|-------------|-----------|----------
Both mowing together | 1 | | x
------------------------------------------------------------
Now we fill in the rates in lawns per minute, That means we
divide the number of lawns mowed by the minutes, which is to
put the number of lawns mowed over the number of minutes:
| Number of | Rate | Time
| lawns | in | to
| mowed | lawns/min | complete
-----------------------|-------------|-----------|----------
Brad mowing alone | 1 | 1/75 | 75
-----------------------|-------------|-----------|----------
Capri mowing alone | 1 | 1/60 | 60
-----------------------|-------------|-----------|----------
Both mowing together | 1 | 1/x | x
------------------------------------------------------------
The equation comes from
Multiply through by LCD of 300x
4x + 5x = 300
9x = 300
x = 
minutes
It would take them minutes mowing together to mow 1 lawn.
Edwin
