SOLUTION: In an hour, Phoenix and Foghorn have munched all of the viral bodies. Phoenix, never one to miss a meal, can eat the same amount of virus by itself. Foghorn, the dainter of the two

Question 203971: In an hour, Phoenix and Foghorn have munched all of the viral bodies. Phoenix, never one to miss a meal, can eat the same amount of virus by itself. Foghorn, the dainter of the two phagoes, can eat the same amount of virus as its twin, but it takes 25 minutes longer.
If phoenix dined alone how long would it take to consume the viral load? How long would it take Foghorn?
Im kinda lost on this one.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
took a while because i'm a little rusty, but i think i have the answer.
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let p = the rate at which phoenix eats virus.
let f = the rate at which foghorn eats virus.
eating together, they can consume all of the virus in 1 hours.
since 1 hour = 60 minutes, we can use minutes rather than hours.
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our equation we have to work with is:

this becomes
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we know that eating alone phoenix can consume the virus in t minutes.
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t is a small letter T not to be confused with the + sign if at all possible.
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our formula for phoenix eating the virus alone is:

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we know that eating alone foghorn can consume the virus in t+25 minutes.
our formula for foghorn eating the virus alone is:

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we can solve for p and f in terms of v and t.

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our equation that we had above of becomes:

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if we divide both sides of this equation by v, then the v cancels out and we are left with:

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if we multiply both sides of this equation by we get:

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that equation becomes:

which becomes

if we subtract 120*t + 1500 from both sides of the equation, we are left with:

i used the quadratic formula to solve this.
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i got:
t = 108.7882534
and
t = -13.78825336 which was rejected because it's negative.
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my answer was t = 108.7882534
this made (t+25) = 133.7882534
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the question to be answered was:
If phoenix dined alone how long would it take to consume the viral load? How long would it take Foghorn?
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t is the time it takes phoenix to eat the virus.
t+25 is the time it takes foghorn to eat the virus.
your answers are:
it takes phoenix 108.7882534 minutes to eat the virus.
it takes foghorn 133.7882534 minutes to eat the virus.
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the rate that phoenix takes to eat the virus is v/108.7882534 = p
the rate that foghorn takes to eat the virus is v/133.7882534 = f
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to prove your answer is correct, substitute in the original equation to see if you get the right answer.
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the original equation is 60 * (f + p) = v
this becomes 60 * (v/108.7882534 + v/133.7882534) = v
this becomes (60*v)/108.7882534 + (60*v)/133.7882534 = v
divide both sides of this equation by v and you get:
(60/108.7882534 + 60/133.7882534 = 1
which becomes:
.551530134 + .448469866 = 1
which becomes:
1 = 1
original equation is true so the answer are good.
your answers again are:
it takes phoenix 108.7882534 minutes to eat the virus.
it takes foghorn 133.7882534 minutes to eat the virus.
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