Word Problem:
Jack mows the lawn in 4 hours, mary mows the lawn in 5 hours. how long will it take them if they mowed the lawn together?
I have a hard time figuring out which formula to use to solve a problem in a word problem can anyone help and tell me how to set up the problem so I can do the math?
Hello Laura,
the method that i would recommend is this simple method (assuming that both of them mow the lawn at a constant speed):
Jack->4h can complete lawn
jack->1h can complete 1/4 lawn
Mary->5h can complete lawn
Mary->1h can complete 1/5 lawn
Together->1h can complete 1/4+1/5=9/20 lawn.
That means that in 1 hour they can complete 9/20 lawn. To figure out time just take 20/20 divide by 9/20, the answer is 2/2/9. Hope that helps ^_^. Of course don't forget to put it in hours! ^_^
The combined rate of lawn mowing is 9/20 lawn/hour. To mow one lawn therefore takes 20/9 hour, or 2 and 2/9 hours.
Deanna's answer was correct but the 2/2/9 at the end was mistyped.
Hello Drwls,
sorry, but i don't understand what you mean by the 2/2/9 at the end was mistyped? Thank you for correcting my mistake if i had made one though! ^_^
Sure! Word problems can be tricky, but don't worry, I'll help you set up the problem and choose the appropriate formula to solve it.
In this case, we want to find how long it would take Jack and Mary to mow the lawn together. Since they are working together, we need to add their individual rates of mowing to find their combined rate.
Let's start by finding Jack's rate. We know that Jack mows the lawn in 4 hours, so his rate of mowing is 1 lawn / 4 hours, or 1/4 lawns per hour.
Next, let's find Mary's rate. We know that Mary mows the lawn in 5 hours, so her rate of mowing is 1 lawn / 5 hours, or 1/5 lawns per hour.
To find their combined rate, we add their individual rates: (1/4 lawns per hour) + (1/5 lawns per hour) = (9/20) lawns per hour.
Now that we know their combined rate, we can set up the equation:
(time taken together) × (combined rate) = 1 lawn.
Let's call the time taken together "t" hours.
So the equation becomes: t × (9/20) = 1.
To solve for t, we can divide both sides of the equation by (9/20):
t = 1 / (9/20).
Now, to simplify, we can multiply by the reciprocal of (9/20), which is (20/9):
t = 1 × (20/9) = 20/9.
Therefore, it would take them 20/9 hours to mow the lawn together.
I hope this explanation helps you understand how to set up and solve word problems like this one! Let me know if you have any further questions or need additional clarification.