You can
put this solution on YOUR website! Please help me to solve : Jack usually mows the lawn in 3 hours. Marilyn can
mow the same yard in 6 hours. How much time would it take for them to mow the
lawn together?
Make this chart: | Number of | | rate in
| lawns mowed | hours | lawns/hr.
---------------------------------------------------------------------
Jack working alone | | |
Marilyn working alone | | |
Jack and Marilyn working together| | |
We want to know the number of hours it will take Jack and Marilyn if they work
together. Let that be x hours to mow 1 lawn so we fill in x for the hours they
will take and 1 for the number of laws they will mow working together.
| Number of | no. of | rate in
| lawns mowed | hours | lawns/hr.
---------------------------------------------------------------------
Jack working alone | | |
Marilyn working alone | | |
Jack and Marilyn working together| 1 | x |
Jack mows 1 lawn in 3 hours, so we fill in 1 for the number of lawns
he mows and 3 for the number of hours it takes him:
Similarly, Marilyn mows 1 lawn in 6 hours, so we fill in 1 for the
number of lawns she mows and 6 for the number of hours it takes her:
| Number of | no. of | rate in
| lawns mowed | hours | lawns/hr.
---------------------------------------------------------------------
Jack working alone | 1 | 3 |
Marilyn working alone | 1 | 6 |
Jack and Marilyn working together| 1 | x |
Next we find the rates in lawns/hr by dividing lawns mowed by hours:
| Number of | no. of | rate in
| lawns mowed | hours | lawns/hr.
---------------------------------------------------------------------
Jack working alone | 1 | 3 | 1/3
Marilyn working alone | 1 | 6 | 1/6
Jack and Marilyn working together| 1 | x | 1/x
The equation comes from:
Jack's rate + Marilyn's rate = their combined rate
1/3 + 1/6 = 1/x
Multiply through by the LCD which is 6x
2x + x = 6
3x = 6
x = 2
So it would take them 2 hours working together.
Edwin
