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

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(39625) (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 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) (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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