Lisa can shovel her driveway in 30 minutes and Tom can shovel his driveway in 40 minutes. How long will it take them to shovel the driveway together?

how much work is done each hour?

1/30 + 1/40 = 1/x

It will take them x hours working together.

Actually, the problem is very poorly worded, since the times are for shoveling their own driveways, and we have no idea which driveway they work on together.

To find out how long it will take Lisa and Tom to shovel the driveway together, we can use the concept of work rate.

First, let's determine the work rate of each person. Work rate is defined as the amount of work done per unit of time.

Lisa's work rate is 1 driveway per 30 minutes, which can be written as 1/30 driveways per minute.
Tom's work rate is 1 driveway per 40 minutes, which can be written as 1/40 driveways per minute.

To find the combined work rate of Lisa and Tom, we can add their individual work rates together:

Lisa's work rate + Tom's work rate = (1/30 + 1/40) driveways per minute

Now, let's simplify this expression. First, we need to find a common denominator:

1/30 + 1/40 = (4/4 * 1/30) + (3/3 * 1/40) = 4/120 + 3/120 = 7/120 driveways per minute

So, the combined work rate of Lisa and Tom is 7/120 driveways per minute.

Now, to find out how long it will take them to shovel the driveway together, we can use the formula:

Time = Work / Rate

We know that the work to be done is 1 driveway, and the combined work rate is 7/120 driveways per minute. Substituting these values into the formula, we get:

Time = 1 driveway / (7/120 driveways per minute)

To divide by a fraction, we can multiply by its reciprocal:

Time = 1 driveway * (120 driveways per minute / 7 driveways) = 120/7 minutes

Simplifying this fraction, we get:

Time = 17.14 minutes

Therefore, it will take Lisa and Tom approximately 17.14 minutes to shovel the driveway together.