SOLUTION: A couple washed the family car in 24 minutes. Previously, when they each had washed the car alone, it took the husband 20 minutes longer than the wife. How long did it take the wif

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A couple washed the family car in 24 minutes. Previously, when they each had washed the car alone, it took the husband 20 minutes longer than the wife. How long did it take the wif      Log On


   

Question 944256: A couple washed the family car in 24 minutes. Previously, when they each had washed the car alone, it took the husband 20 minutes longer than the wife. How long did it take the wife to wash the car?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
( 1 car / 24 min ) is their rate working together
Let +t+ = wife's time to wash the car working alone
+t+%2B+20+ = husband's time working alone
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+1%2Ft+%2B+1%2F%28+t%2B20+%29+=+1%2F24+
Multiply both sides by +24t%2A%28+t+%2B+20+%29+
+24%2A%28+t+%2B+20+%29+%2B+24t+=+t%2A%28+t+%2B+20+%29+
+24t+%2B+480+%2B+24t+=+t%5E2+%2B+20t+
+t%5E2+-+28t+-+480+=+0+
Use the quadratic formula
+t+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-28+
+c+=+-480+
+t+=+%28+-%28-28%29+%2B-+sqrt%28+%28-28%29%5E2+-+4%2A1%2A%28-480%29+%29%29+%2F+%282%2A1%29+
+t+=+%28+28+%2B-+sqrt%28+784+%2B+1920+%29%29+%2F+2+
+t+=+%28+28+%2B-+sqrt%28+2704+%29%29+%2F+2+ ( can't use negative square root )
+t+=+%28+28+%2B+52+%29+%2F+2+
+t+=+80%2F2+
+t+=+40+
+t+%2B+20+=+60+
Wife takes 40 min to wash car
Husband takes 1 hr
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check:
+1%2Ft+%2B+1%2F%28+t%2B20+%29+=+1%2F24+
+1%2F40+%2B+1%2F60+=+1%2F24+
+3%2F120+%2B+2%2F120+=+5%2F120+
+5+=+5+
OK