Mr. Bailey mowed his yard in 90 minutes. His son Roy mows the yard in 75 minutes. How long will it take them if they work together (using 2 lawn mowers)?
1/x = 1/90 + 1/75
x = 40.9
How to set up an equation for this problem? Thank you.
You have to ask yourself how much work gets done in 1 minute.
Mr Baily can do 1/90 of the total in a minute.
Add to that the amount that his son does in a minute.
The sum is how much of the job gets done by both together.
SO, if 1/3 gets done in a minute, the job takes 3 minutes. That's why the 1/x is used; it is the fraction that gets done each minute by all workers. You can have more terms.
If Paul comes over to help, and he can do the lawn in 80 minutes, then
1/x = 1/90 + 1/70 + 1/80
This is the way to set up all these work problems.
Thank
To find out how long it will take them to mow the yard together, we can use the concept of work rates.
Mr. Bailey can mow the yard in 90 minutes, which means his work rate is 1 yard per 90 minutes, or 1/90 yard per minute.
Similarly, his son Roy can mow the yard in 75 minutes, so his work rate is 1/75 yard per minute.
When they work together, their work rates are additive. So, the total work rate when they mow together is:
1/90 + 1/75 = (75 + 90) / (90 * 75) = 165 / 6750 = 1/45 yard per minute.
Now that we know their combined work rate, we can find out how long it will take them to mow the yard together. Let's call this time x.
Since their combined work rate is 1/45 yard per minute, we can write the equation:
1/45 * x = 1 yard,
where x is the time it takes for them to mow the yard together in minutes.
Solving for x, we get:
x = 45 minutes.
Therefore, it will take them 45 minutes to mow the yard together if they both use 2 lawn mowers.