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The junior senator can do a labyrinth in 50 minutes. The senior senator can do a labyrinth in 30 minutes.  Working together, how many minutes would it take them to work their way through 12 labyrinths?

 Dec 21, 2021
 #1
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In 1 minute, the junior senator can work through 1/50 labyrinth.

The senior senator can work through 1/30 labyrinth in a minute.

Thus, if they work together, they will be done with 1/30 + 1/50 = 4/75 of a labyrinth in a minute. This means that they need to work for 75/4 minutes to finish the whole labyrinth. Multiply this by 12, getting 225 minutes.

 Dec 21, 2021
 #2
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12 / ( 1/50 + 1/30) =   12/ (8/150) = 225 minutes      (as TFH found)

 Dec 21, 2021

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