t = the number of hours Henry needs to clean the pool alone

1/t pool per hour is Henry's rate

3t = the number of hour John needs to clean the pool alone (Henry is 3 times as fast as John, or John is 3 times as slow as Henry).

1/(3t) = 1/(3t) pool per hour is John's rate

1/2 pool per hour is the together rate

The sum of the rates of Henry and John equals the together rate:

1/t + 1/(3t) = 1/2 (the equation we use to find the number of hours for Henry)

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click here to see the equation solved for t

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t = 8/3 hr

t = 2 1/3 hr

t = 2 hr 60/3 min

t = 2 hr 20 min

Henry needs 2 hours and 20 minutes to clean the pool alone.