Question

question 3
two people are mowing a large lawn. one person has a riding lawnmower, and the other person has a push mower. the person with the riding mower can cut the lawn alone in 4 hours, and the person with the push mower can cut the lawn alone in 7 hours. how long does it take for them, working together, to cut the lawn? (fractional answers are ok.)
the riding mower cutting rate is \boxed{} per hour.
the push mower cutting rate is \boxed{} per hour.
the combined cutting rate is \boxed{} per hour.
it will take them \boxed{} hour(s) to cut the lawn together.

Explanation:

Step1: Find riding mower rate

The riding mower can complete 1 lawn in 4 hours. Rate = work / time, so rate is $\frac{1}{4}$ per hour.

Step2: Find push mower rate

The push mower can complete 1 lawn in 7 hours. So rate is $\frac{1}{7}$ per hour.

Step3: Find combined rate

Add the two rates: $\frac{1}{4} + \frac{1}{7} = \frac{7 + 4}{28} = \frac{11}{28}$ per hour.

Step4: Find time together

Time = work / combined rate. Work is 1 lawn, so time = $1 \div \frac{11}{28} = \frac{28}{11}$ hours.

Answer:

The riding mower cutting rate is $\frac{1}{4}$ per hour.
The push mower cutting rate is $\frac{1}{7}$ per hour.
The combined cutting rate is $\frac{11}{28}$ per hour.
It will take them $\frac{28}{11}$ hour(s) to cut the lawn together.