Please solve this equation for me! :)

[Heather Feather]

I'm new to this message board and this is my first post so...yeah XD

I need this rational equation work problem to be solved:

A town's old street sweeper can clean the streets in 60 hours. The new street sweeper can clean the streets in 20 hours. How long would it take the old and the new sweeper to clean the streets together?

Lol. Work problems make me confuzzled :roll: Please help me! Thank you

~*'...'*~ r00 r00 (lol that's my nick name XD)

 

[soroban]

Hello, XD!

A town's old street sweeper can clean the streets in 60 hours.
The new street sweeper can clean the streets in 20 hours.
How long would it take the old and the new sweeper to clean the streets together?

You can baby-talk your way through most Work problems.

Let x = number of hours for both to do the job.

The old sweeper takes 60 hours to do the job.
. . . In one hour, it can do 1/60 of the job.
. . . In x hours, it can do x/60 of the job.

The new sweeper takes 20 hours to do the job.
. . . In one hour, it can do 1/20 of the job.
. . . In x hours, it can do x/20 of the job.

Together, in x hours, then can do: .x/60 + x/20 of the job.
. . . But this is the whole job . . . 1 job.

And there> is our equation: . x/60 + x/20 . = . 1

Multiply through by 60: . x + 3x . = . 60
. . . . . . . . . . . . . . . . . . . . . . .4x . = . 60
. . . . . . . . . . . . . . . . . . . . . . . .x . = . 15

Therefore, it will take 15 hours with both sweepers on the job.

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<u>Check</u>

The old sweeper does 1/60 of the job per hour.
. . . In 15 hours, it does 15/60 = 1/4 of the job.

The new sweeper does 1/20 of the job per hour.
. . . In 15 hours, it does 15/20 = 3/4 of the job.

Together, they do 1/4 + 3/4 = 1 . . . the whole job.

 

[Heather Feather]

:shock: wow.

:lol: THANK YOOOOOOOOOOOOU!! *huggles* YOUR THE BEST! I am forever greatful I get how to do it now!

:wink: Expect to help me more later XD :roll: