SOLUTION: A boy counts toads at 22/min and then frogs at 18/min. He counts for a total of 4 mins and realizes that he has counted an equal number of toads and frogs. How long did he count

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Question 757654: A boy counts toads at 22/min and then frogs at 18/min. He counts for a total of 4 mins and realizes that he has counted an equal number of toads and frogs. How long did he count toads?
I know he counted frogs longer because they are slower. I know he counted toads at 4/min faster.
?
Found 2 solutions by josgarithmetic, stanbon:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
That's an interesting new uniform-rates problem.

So there were counting reptiles. Each reptile is counted at a different rate. r*t=q using r for rate in reptile per minute, t is time in minutes, q is the count of reptiles whether frog or toad.

Which Reptile_______________rate______________time_____________count
TOADS_______________________22________________(___)____________q
FROGS_______________________18________________(___)____________q

We only know that q is the same for both kinds. We know the total time counting was 4 minutes but not yet how much time for each kind of reptile. We can make expressions for each.

Which Reptile_______________rate______________time_____________count
TOADS_______________________22________________(q/22)____________q
FROGS_______________________18________________(q/18)____________q
Total_________________________________________4_________________2q

We use the found equation of highlight%28q%2F22%2Bq%2F18=4%29 and solve for q. You can easily compute the time for the counting of each reptile, just using the time expression as shown. Remember, q is for the number of each reptile counted.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A boy counts toads at 22/min and then frogs at 18/min.
He counts for a total of 4 mins and realizes that he has counted an equal number of toads and frogs. How long did he count toads?
I know he counted frogs longer because they are slower. I know he counted toads at 4/min faster.
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Equation:
(22/min)(x min) = (18/min)(4-x) min
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22x = 72-18x
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40x = 72
x = 1.8 min (time during which he counted toads)
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4-x = 2.2 min (time during which he counted frogs)
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Cheers,
Stan H.
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