SOLUTION: You and your sibling decide to mow the grass for your parents. You take the riding mower, while your sibling uses the push mower. You can mow 3.5 hours faster than your sibling. To

Algebra ->  Rate-of-work-word-problems -> SOLUTION: You and your sibling decide to mow the grass for your parents. You take the riding mower, while your sibling uses the push mower. You can mow 3.5 hours faster than your sibling. To      Log On


   

Question 1128731: You and your sibling decide to mow the grass for your parents. You take the riding mower, while your sibling uses the push mower. You can mow 3.5 hours faster than your sibling. Together you both get done within 2 3/4hours. How long would it take each of you working alone?
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hrs using the push mower
+t+-+3.5+ = time in hrs using riding mower
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+1%2Ft+%2B+1%2F%28+t+-+3.5+%29+=+1+%2F+2.75+
Multiply by +t%2A%28+t+-+3.5+%29%2A2.75+
+2.75%2A%28+t+-+3.5+%29+%2B+2.75t+=+t%2A%28+t+-+3.5+%29+
+2.75t+-+9.625+%2B+2.75t+=+t%5E2+-+3.5t+
+t%5E2+-+9t+%2B+9.625+=+0+
+1000t%5E2+-+9000t+%2B+9625+=+0+
+8t%5E2+-+72t+%2B+77+=+0+
Use quadratic formula, find +t+ and +t+-+3.5+Get a 2nd
opinion if needed

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

You and your sibling decide to mow the grass for your parents. You take the riding mower, while your sibling uses the push mower. You can mow 3.5 hours faster than your sibling. Together you both get done within 2 3/4hours. How long would it take each of you working alone?
Let my time be M

Then time my sibling takes is M + 3.5

We then get: matrix%281%2C3%2C+1%2FM+%2B+1%2F%28M+%2B+3.5%29%2C+%22=%22%2C+1%2F%2811%2F4%29%29

matrix%281%2C3%2C+1%2FM+%2B+1%2F%28M+%2B+3.5%29%2C+%22=%22%2C+4%2F11%29

11(M + 3.5) + 11M = 4M(M + 3.5) ------- Multiplying by LCD, 11M(M + 3.5)

matrix%281%2C3%2C+11M+%2B+38.5+%2B+11M%2C+%22=%22%2C+4M%5E2+%2B+14M%29

matrix%281%2C3%2C+4M%5E2+%2B+14M+-+22M+-+38.5%2C+%22=%22%2C+0%29

matrix%281%2C3%2C+4M%5E2+-+8M+-+38.5%2C+%22=%22%2C+0%29

matrix%281%2C3%2C+8M%5E2+-+16M+-+77%2C+%22=%22%2C+0%29 ------- Multiplying by 2 to get rid of the decimal

Solve the above quadratic equation for M, my time

Add 3.5 to that number to get my sibling's time.