SOLUTION: When a boy use toy to shovel to help his mother the driveway the job take 4 hours if the boy were alone it would take him 4 times longer than it would his mother ..how long would

Algebra ->  Equations -> SOLUTION: When a boy use toy to shovel to help his mother the driveway the job take 4 hours if the boy were alone it would take him 4 times longer than it would his mother ..how long would      Log On


   



Question 1022734: When a boy use toy to shovel to help his mother the driveway the job take 4 hours if the boy were alone it would take him 4 times longer than it would his mother ..how long would it take the boy's mother to shovel the driveway alone ?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +R%5B1%5D+ = the mother's rate of shoveling in
[ driveways ] / [ hr ]
+R%5B1%5D%2F4+ = the son's rate of shoveling in
[ driveways ] / [ hr ]
+1%2F4+ = their rate shoveling together
[ 1 driveway ] / [ 4 hrs ]
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Add their rates of shoveling to get their rate
of shoveling together
+R%5B1%5D+%2B+R%5B1%5D%2F4+=+1%2F4+
+4R%5B1%5D+%2B+R%5B1%5D+=+1+
+5R%5B1%5D+=+1+
+R%5B1%5D+=+1%2F5+
It would take the mother 5 hrs to shovel alone
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check:
+R%5B1%5D+%2F+4+=+%281%2F5%29+%2F+4+
+R%5B1%5D+%2F+4+=+1%2F20+
Her son would take 20 hrs shoveling alone
+R%5B1%5D+%2B+R%5B1%5D%2F4+=+1%2F4+
+1%2F5+%2B+1%2F20+=+1%2F4+
+4%2F20+%2B+1%2F20+=+5%2F20+
+5%2F20+=+5%2F20+
OK