Keenan is training for a triathlon and needs to swim a certain distance for today's workout. If he swims at the rec center pool, he will complete a 118-yard warmup and then swim laps in a lane that is 41 yards long. If Keenan swims at the indoor pool at his gym, he will complete a 154-yard warmup, plus a main set that consists of 32 yards per lap. If Keenan swims the correct number of laps, he can complete the same distance in either pool. How many laps will that take? How long will Keenan's workout be in total?

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Step-by-step explanation:

For n laps, the length Keenan swims in the rec center pool is ...

  118 + 41n

and the length he swims in the gym pool is ...

  154 +32n

These are equal length for equal numbers of laps, so we have ...

  118 + 41n = 154 + 32n

  9n = 36 . . . . . . . . . . . . . subtract 32n+118

  n = 4 . . . . . . . . divide by 9

Then the length of Keenan's workout is ...

  118 +41(4) = 282 . . . . yards

It will take 4 laps to make the workout total 282 yards in each pool.

step-by-step explanation:

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