Help creating equation for word prob: "Mike can plow field in 12 hrs; Phil in 15 hrs"

[ricco333]

Help creating equation for word prob: "Mike can plow field in 12 hrs; Phil in 15 hrs"

Hi, my daughter is in 7th grade and starting Algebra 1, she got the first assignment and asked for my help but it has been so long I'm kinda lost. The exercises ask to create an equation and solve, I need help with the equation part.
This is the word problem:

"Mike can plow a field in 12 hours and his brother Phil can plow it in 15 hours. How long will it take them to plow it if they use 2 plows and work together?"


...and here is another one but I think is the opposite:


"Mary can make a costume twice as fast as Sam can. if they both work together they can make it in 6 hours. how long will it take Mary to make the costume if she works alone?"

Thanks very much for your help!

Erik

 

[Denis]

Hmmm....is your daughter able to add fractions: 1/12 + 1/15 = ?

 

[Dr.Peterson]

Hi, my daughter is in 7th grade and starting Algebra 1, she got the first assignment and asked for my help but it has been so long I'm kinda lost. The exercises ask to create an equation and solve, I need help with the equation part.
This is the word problem:

"Mike can plow a field in 12 hours and his brother Phil can plow it in 15 hours. How long will it take them to plow it if they use 2 plows and work together?"


...and here is another one but I think is the opposite:


"Mary can make a costume twice as fast as Sam can. if they both work together they can make it in 6 hours. how long will it take Mary to make the costume if she works alone?"

Thanks very much for your help!

Erik

There are a few different ways to work these out, some of which don't really require algebra and equations. I would not expect these to be given to someone just beginning algebra; and I would expect that some examples were given to show how to apply algebra to them (that is, showing the method they expect). Have you looked at those examples and tried to follow them?

One approach that is likely to be what they want is to think in terms of rates. How many fields per hour can each person plow? Working together, they will work at the sum of those rates. You can either work with that combined rate, or which each rate separately, with the equation "rate times time = amount done".

Check the book or notes, and either make an attempt at one of these equations based on the example and show us what you've done, or just show the example. Either way, we will then be able to guide you along a method that matches what is being taught, rather than something else that might just confuse you.

The second problem will have the same kind of equation, but with the variable in a different place. We should work on that only after we've figured out the first.

 

[ricco333]

Hmmm....is your daughter able to add fractions: 1/12 + 1/15 = ?

Thanks for the reply, yes she is able to, I just couldn't figure out how to solve for that I thought it was like the average equation 12+15 then divided by 2.

Is the 2nd exercise also the same?
Again, thanks a million she is super why and most of the time asking the Math teacher is a bigger challenge.

Erik

 

[ricco333]

There are a few different ways to work these out, some of which don't really require algebra and equations. I would not expect these to be given to someone just beginning algebra; and I would expect that some examples were given to show how to apply algebra to them (that is, showing the method they expect). Have you looked at those examples and tried to follow them?

One approach that is likely to be what they want is to think in terms of rates. How many fields per hour can each person plow? Working together, they will work at the sum of those rates. You can either work with that combined rate, or which each rate separately, with the equation "rate times time = amount done".

Check the book or notes, and either make an attempt at one of these equations based on the example and show us what you've done, or just show the example. Either way, we will then be able to guide you along a method that matches what is being taught, rather than something else that might just confuse you.

The second problem will have the same kind of equation, but with the variable in a different place. We should work on that only after we've figured out the first.

I'm going to check her math binder for class notes but as AFAIK no examples were given, the math teacher just posted the assignment via Edmodo yesterday.

Thanks.

Erik

 

[ricco333]

Hmmm....is your daughter able to add fractions: 1/12 + 1/15 = ?

Yes she is, thanks for the help, she did the math and the answer is .15 I'll work with her the remaining exercises.

Thanks.

 

[mmm4444bot]

You'll find dozens of lessons, videos and examples, by googling keyphrase: how to solve work problems in algebra :cool:

 

[Harry_the_cat]

These questions expect a lot from a beginning algebra student.

You might find it helpful for these "rates" questions to set up a table like the following:

	Mike	Phil	Together
Time to plow field (hours)	12	15	Doesn't make sense to add the times.
Rate (fields per hour)	\(\displaystyle \frac{1}{12}\)	\(\displaystyle \frac{1}{15}\)	Makes sense to add the rates \(\displaystyle \frac{1}{12}+\frac{1}{15}\)

So, working together their rate is \(\displaystyle \frac{1}{12}+\frac{1}{15} = \frac{3}{20}\) fields per hour.

This is the same as \(\displaystyle \frac{20}{3}\) hours per field. That is 6 hours 40 min.

Try the second one using a similar method. Use the table below:

	M	S	Together
Time (hours)	You will need to introduce a variable x here.	What is this in terms of x?	Does it make sense to add the times?
Rate (costumes per hour)			Does it make sense to add the rates?

 

[Steven G]

Hi, my daughter is in 7th grade and starting Algebra 1, she got the first assignment and asked for my help but it has been so long I'm kinda lost. The exercises ask to create an equation and solve, I need help with the equation part.
This is the word problem:

"Mike can plow a field in 12 hours and his brother Phil can plow it in 15 hours. How long will it take them to plow it if they use 2 plows and work together?"


...and here is another one but I think is the opposite:


"Mary can make a costume twice as fast as Sam can. if they both work together they can make it in 6 hours. how long will it take Mary to make the costume if she works alone?"

Thanks very much for your help!

Erik

See examples at https://www.youtube.com/watch?v=wy8NsCmWdsU&list=PLtmopxjCQWiwmyQMbd8Y7tZ2ot6x2_clX&index=39
View the video starting at 23:03

 

[Denis]

Mike can plow a field in 12 hours and his brother Phil can plow it in 15 hours.
How long will it take them to plow it if they use 2 plows and work together?"

I find there easier when changed to ye olde speed = distance/time.

Mike walks 60 miles in 12 hours.
Phil walks 60 miles in 15 hours.
Jomo walks 60 miles at Mike's speed + Phil's speed.
How long does it take Jomo?

Mike's speed = 60/12 = 5 mph
Phil's speed = 60/15 = 4 mph

Jomo's time = 60/(5 + 4) = 60/9 = 6 2/3 hours

 

[sinx]

Hi, my daughter is in 7th grade and starting Algebra 1, she got the first assignment and asked for my help but it has been so long I'm kinda lost. The exercises ask to create an equation and solve, I need help with the equation part.
This is the word problem:

"Mike can plow a field in 12 hours and his brother Phil can plow it in 15 hours. How long will it take them to plow it if they use 2 plows and work together?"


...and here is another one but I think is the opposite:


"Mary can make a costume twice as fast as Sam can. if they both work together they can make it in 6 hours. how long will it take Mary to make the costume if she works alone?"

Thanks very much for your help!

Erik

[in addition to the help others have given.]
it is not easy to see what to do, so draw a picture, (of a field, shading in the amt plowed by each person).
then you can see one person plows 1/12 of the field in one hour, the other 1/15. Add them and you have the amt plowed, in fields/hour. Then to get hours/field, you flip the fraction upside down (reciprocal).