SOLUTION: jacqui commutes 30 miles to her job each day. She finds that if she drives 10 miles/hour faster, it takes her 6 minutes less to get to work .find her new speed

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Question 258761: jacqui commutes 30 miles to her job each day. She finds that if she drives 10 miles/hour faster, it takes her 6 minutes less to get to work .find her new speed
Found 2 solutions by richwmiller, stanbon:
Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website!
rt=30
t=30/r
(r+10)(t-1/10)=30
(r+10)(30/r-1/10)=30
r=50
new speed 50+10=60
60(t-1/10)=30
t=3/5=36/60= 36 minutes
t-1/10=new time 30 minutes

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
jacqui commutes 30 miles to her job each day. She finds that if she drives 10 miles/hour faster, it takes her 6 minutes less to get to work.
find her new speed
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Old DATA:
distance = 30 miles ; rate = x mph ; time = d/r = 30/x hrs.
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New DATA:
distance = 30 miles ; rate = (x+10) mph ; time = d/r = 30/(x+10) hrs
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Equation:
old time - new time = 1/10 hr
30/x - 30/(x+10) = 1/10
Multiply thru by 10x(x+10)
300(x+10) - 300x = x(x+10)
3000 = x^2 + 10x
---
x^2 + 10x - 3000 = 0
(x+60)(x-50) = 0
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Positive solution:
x = 50 mph (old speed)
---
x+10 = 60 mph (her new speed)
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Cheers,
Stan H.