SOLUTION: If 15 oxen or 20 cows can eat the grass of a field in 80 days, then in how many days will 6 oxen and 2 cows eat the same grass?

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Question 936926: If 15 oxen or 20 cows can eat the grass of a field in 80 days, then in how many days will 6 oxen and 2 cows eat the same grass?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+15+ oxen eat ( 1 field ) / ( 80 days )
+1+ ox eats ( 1 field ) / ( 15*80 days )
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+20+ cows eat ( 1 field ) / ( 80 days )
+1+ cow eats ( 1 field ) / ( 20*80 days )
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Add their rates of eating to get their rate eating together
Let their rate eating together = ( 1 field ) / ( d days )
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+6%2A%28+1%2F1200+%29+%2B+2%2A%28+1%2F1600+%29+=+1%2Fd+
Multiply both sides by +4800d+
+24d+%2B+6d+=+4800+
+30d+=+4800+
+d+=+160+
6 oxen and 2 cows eat 1 field of grass in 160 days
check:
+6%2A%28+1%2F1200+%29+%2B+2%2A%28+1%2F1600+%29+=+1%2Fd+
+6%2A%28+1%2F1200+%29+%2B+2%2A%28+1%2F1600+%29+=+1%2F160+
Multiply both sides by +40+
+6%2F30+%2B+2%2F40+=+1%2F4+
+1%2F5+%2B+1%2F20+=+5%2F20+
+4%2F20+%2B+1%2F20+=+5%2F20+
OK