Where does the 360 come from?

[Ust]

Here is the question:

Jane can mow a lawn in 2 hours. Henry can mow the same lawn in 1.5 hours. About how long will it take to mow the lawn if Jane and Henry worked together?

Here is the solution:
To solve this equation change the hours to minutes and set up the following equations.

x/120 + x/90 = 1

Multiply by 360. 3x + 4x = 360, so x = 51.

I don't understand where the 360 comes from. Do you just pick a random number to multiply?

 

[Deleted member 4993]

Here is the question:

Jane can mow a lawn in 2 hours. Henry can mow the same lawn in 1.5 hours. About how long will it take to mow the lawn if Jane and Henry worked together?

Here is the solution:
To solve this equation change the hours to minutes and set up the following equations.

x/120 + x/90 = 1

Multiply by 360. 3x + 4x = 360, so x = 51.

I don't understand where the 360 comes from. Do you just pick a random number to multiply?

Can you add:

1/3 + 1/4

Same principle....

 

[pinnaclestudies]

Lcm

It's the Least Common Multiple (LCM) and is used to add or subtract fractions

 

[MarkFL]

Here is the question:

Jane can mow a lawn in 2 hours. Henry can mow the same lawn in 1.5 hours. About how long will it take to mow the lawn if Jane and Henry worked together?

Here is the solution:
To solve this equation change the hours to minutes and set up the following equations.

x/120 + x/90 = 1

Multiply by 360. 3x + 4x = 360, so x = 51.

I don't understand where the 360 comes from. Do you just pick a random number to multiply?

Another approach:

In 6 hours, Jane can mow 3 lawns and Henry can mow 4 lawns, so together they can mow 7 lawns. That's 6 hours for 7 lawns, or 6/7 of an hour per lawn. This is roughly 51 minutes 26 seconds.