mary takes 3 hours to mow the yard. it takes sally 5 hours. how long would it take with them mowing it together? give the exact decimal answer.

There are many ways to do this, but what I would like to do here is 1/3 + 1/5= 1/?

1.7

To find the amount of time it would take for Mary and Sally to mow the yard together, we can use the concept of rates.

First, let's determine how much of the yard each person can mow in one hour. We can calculate this by dividing the total yard length by the number of hours it takes each person individually.

Mary's rate (yards per hour) = 1 yard / 3 hours = 1/3 yard per hour
Sally's rate (yards per hour) = 1 yard / 5 hours = 1/5 yard per hour

To determine how long it would take for them to mow the yard together, we need to add their rates.
Combined rate (yards per hour) = Mary's rate + Sally's rate = 1/3 + 1/5 yard per hour

Now, we need to find the reciprocal of the combined rate to determine how many hours it would take for them to mow the entire yard together.
Combined rate (hours per yard) = 1 / (1/3 + 1/5) hours per yard

To find the sum of the fractions (1/3 + 1/5), we need a common denominator. The least common multiple of 3 and 5 is 15.

Combined rate (hours per yard) = 1 / (5/15 + 3/15) hours per yard
= 1 / (8/15) hours per yard

To divide by a fraction, we multiply by the reciprocal of the fraction (flip numerator and denominator).

Combined rate (hours per yard) = 1 * (15/8) hours per yard
= 15/8 hours per yard

So, it would take them 15/8 or 1.875 hours to mow the yard together.