Answer :
Answer:
It takes them approximately 27 minutes to mow the lawn if they are working together.
Step-by-step explanation:
Wilma can mow a lawn in 80 minutes. This means she can mow at the rate of 1 lawn in 80 minutes. We can write this rate as R = 1/80
Melissa can mow the same lawn in 40 minutes. This means she can mow at the rate of 1 lawn in 40 minutes. We write the rate as R = 1/40.
Now, if the are working together, we need to determine how long it would take for them to mow a lawn. Let this rate be 1/x.
What we want to find is
1/80 + 1/40 = 1/x
Multiply through by 80, we have
1 + 2 = 80/x
3 = 80/x
Take reciprocals of both sides
x/80 = 1/3
x = 80/3
= 1600 seconds
Approximately 27 minutes
Final answer:
Wilma and Melissa can mow a lawn together in 80/3 or 26 2/3 minutes. The rate of work was determined by summing their individual mowing rates and taking the reciprocal.
Explanation:
To find out how long it will take both Wilma and Melissa to mow the lawn when working together, we need to add their rates of work. Wilma can mow a lawn in 80 minutes, which means her rate is 1/80 of the lawn per minute. Melissa can mow the same lawn in 40 minutes, so her rate is 1/40 of the lawn per minute. To find the combined rate, we add these rates together:
1/80 + 1/40 = 1/80 + 2/80 = 3/80
Thus, together they can mow 3/80 of the lawn per minute. To find how long it takes to mow the entire lawn, we take the reciprocal of their combined rate:
80/3 minutes
Therefore, Wilma and Melissa together can mow the lawn in 80/3 or 26 2/3 minutes when they work together. This is the reduced fraction representing the total time to mow the lawn.
