document.write( "Question 339663: A goat and a sheep can eat all the grass on a field in 90 days. A sheep and a cow can eat all the grass on the field in 60 days. A cow and a goat can eat all the grass on the field in 45 days. So...if I release all the animals on the field, how long will it take them to eat all the grass? \n" ); document.write( "
Algebra.Com's Answer #243533 by ankor@dixie-net.com(22740)\"\" \"About 
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A goat and a sheep can eat all the grass on a field in 90 days.
\n" ); document.write( " A sheep and a cow can eat all the grass on the field in 60 days.
\n" ); document.write( " A cow and a goat can eat all the grass on the field in 45 days.
\n" ); document.write( " So...if I release all the animals on the field, how long will it take them to eat all the grass?
\n" ); document.write( ":
\n" ); document.write( "Let g = time for goat alone to consume all the grass
\n" ); document.write( "Let s = time for sheep to do the same
\n" ); document.write( "Let c = time for cow to do it
\n" ); document.write( ":
\n" ); document.write( "Let the completed job = 1 (all grass consumed)
\n" ); document.write( ":
\n" ); document.write( "Write an equation for each statement:
\n" ); document.write( ":
\n" ); document.write( "\"A goat and a sheep can eat all the grass on a field in 90 days.\"
\n" ); document.write( "\"90%2Fg\" + \"90%2Fs\" = 1
\n" ); document.write( ":
\n" ); document.write( "\" A sheep and a cow can eat all the grass on the field in 60 days.\"
\n" ); document.write( "\"60%2Fs\"+ \"60%2Fc\" = 1
\n" ); document.write( ":
\n" ); document.write( "\"A cow and a goat can eat all the grass on the field in 45 days.\"
\n" ); document.write( "\"45%2Fc\" + \"45%2Fg\" = 1
\n" ); document.write( ":
\n" ); document.write( "Let's use elimination method here, rearrange and multiply the last two equations
\n" ); document.write( "by 1.5 and -2
\n" ); document.write( ":
\n" ); document.write( "\"90%2Fg\" + \"90%2Fs\" + \"%280%29\" = 1
\n" ); document.write( "\"%280%29\" + \"90%2Fs\" = \"90%2Fc\" = 1.5; multiplied by 1.5
\n" ); document.write( "\"-90%2Fg\" + \"%280%29\" = \"-90%2Fc\" = -2; multiplied by -2
\n" ); document.write( "--------------------------------------------- adding eliminates g & c, find s
\n" ); document.write( "0 + \"180%2Fs\" + 0 = .5
\n" ); document.write( ".5s = 180
\n" ); document.write( "s = 360 days for the sheep alone to consume the grass
\n" ); document.write( ":
\n" ); document.write( "Find g using: \"90%2Fg\" + \"90%2Fs\" = 1
\n" ); document.write( "\"90%2Fg\" + \"90%2F360\" = 1
\n" ); document.write( "\"90%2Fg\" + .25 = 1
\n" ); document.write( "\"90%2Fg\" = 1 -.25
\n" ); document.write( "\"90%2Fg\" = .75
\n" ); document.write( ".75g = 90
\n" ); document.write( "g = \"90%2F.75\"
\n" ); document.write( "g = 120 days for goat alone to devour all the grass
\n" ); document.write( ":
\n" ); document.write( "Find c using: \"45%2Fc\" + \"45%2Fg\" = 1
\n" ); document.write( "\"45%2Fc\" + \"45%2F120\" = 1
\n" ); document.write( "\"45%2Fc\" + .375 = 1
\n" ); document.write( "\"45%2Fc\" = 1 - .375
\n" ); document.write( "\"45%2Fc\" + .625
\n" ); document.write( ".625c = 45
\n" ); document.write( "c = \"45%2F.625\"
\n" ); document.write( "c = 72 days for the cows to eat up the grass
\n" ); document.write( ":
\n" ); document.write( "So...if I release all the animals on the field, how long will it take them to eat all the grass?
\n" ); document.write( ":
\n" ); document.write( "Let t = time for all the animals to clear the field
\n" ); document.write( "\"t%2F360\" + \"t%2F120\" + \"t%2F72\" = 1
\n" ); document.write( "Multiply by 1800 to clear the denominators, resulat
\n" ); document.write( "5t + 15t + 25t = 1800
\n" ); document.write( "45t = 1800
\n" ); document.write( "t = \"1800%2F45\"
\n" ); document.write( "t = 40 days for all the animals to eat all the grass.
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "I'm going to send this off without a check, looks like a tornado is in the area here, we will probably lose power. \n" ); document.write( "
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