Jack usually mows his law in 5 hours. Marilyn can mow the same law in 6 hours. How much time would it take for them to mow the lawn together?
Add the RATES that they mow lawns.
1/6 lawn/h + 1/5 lawn/h = 11/30 lawn/h
The combined rate times the time reT equals one lawn
11/30 * T = 1 lawn
T = 30/11 hours
Add the RATES that they each mow lawns.
1/6 lawn/h + 1/5 lawn/h = 11/30 lawn/h
The combined rate times the time required, T, equals one lawn
11/30 * T = 1 lawn
T = 30/11 hours
To find out how much time it would take for them to mow the lawn together, we can use the concept of rates.
First, we need to find the individual rates at which Jack and Marilyn mow the lawn. Jack mows the lawn in 5 hours, so his rate is 1/5 lawns per hour. Marilyn mows the same lawn in 6 hours, so her rate is 1/6 lawns per hour.
When they work together, their rates are additive. Therefore, the combined rate at which they mow the lawn is (1/5 + 1/6) lawns per hour.
Now we can calculate the time it would take for them to mow the lawn together by inverting their combined rate:
Time = 1 / Combined Rate
Substituting the combined rate:
Time = 1 / (1/5 + 1/6)
To simplify, we find the common denominator of 5 and 6, which is 30:
Time = 1 / (6/30 + 5/30)
Time = 1 / (11/30)
To divide by a fraction, we can multiply by its reciprocal:
Time = 1 * (30/11)
Time = 30/11
Therefore, it would take them approximately 2.73 hours, or 2 hours and 44 minutes, to mow the lawn together.