SOLUTION: Jacqui commutes 30 mi to her job each day.She finds that if she drives 10mi/faster, it takes her 6min less to get to work. Find her new speed!

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Question 1078135: Jacqui commutes 30 mi to her job each day.She finds that if she drives 10mi/faster, it takes her 6min less to get to work. Find her new speed!
Found 3 solutions by josgarithmetic, MathTherapy, rothauserc:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Jacqui commutes 30 mi to her job each day.She finds that if she drives 10mi/ MILES per HOUR faster, it takes her 6 minutes less to get to work. Find her new speed!
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The time difference of 6 minutes is 1%2F10 of an hour. 
             SPEED       TIME              DISTANCE
REGULAR        r        30%2Fr             30
NEW          r+10       30%2F%28r%2B10%29        30
DIFFERENCE               1%2F10


30%2Fr-30%2F%28r%2B10%29=1%2F10-----Solve this for r, and evaluate r+10.



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A LITTLE MORE DIRECT
                   SPEED      TIME        DISTANCE
REGULAR             x-10      30/(x-10)     30
NEW                  x        30/x          30
DIFFERENCE                    1/10

Solve for x:
highlight_green%2830%2F%28x-10%29-30%2Fx=1%2F10%29

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

Jacqui commutes 30 mi to her job each day.She finds that if she drives 10mi/faster, it takes her 6min less to get to work. Find her new speed!
Let NEW SPEED be S

Then old speed = S – 10

We then get the following TIME equation: 

30(10)(S – 10) = 30(10S) – S(S – 10) ------- Multiplying by LCD, 10S(S – 10)

300S+-+%223%2C000%22+=+300S+-+S%5E2+%2B+10S

S%5E2+-+300S+-+10S+%2B+300S+-+%223%2C000%22+=+0

S%5E2+-+10S+-+%223%2C000%22+=+0

(S - 60)(S + 50) = 0

S, or new speed = highlight_green%28matrix%281%2C2%2C+60%2C+mph%29%29		OR            S = - 50 (ignore)

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
rate(r) * time (t) = distance
:
1) r * t = 30
2) (r+10) * (t-0.1) = 30
:
By equation 1, t = 30/r
:
(r + 10) * (30/r-0.1) = 30
:
(r + 10) * (30-0.1r)/r = 30
:
(r+10) * (30-0.1r) = 30r
:
0.1r^2 +r -300 = 0
:
r^2 +10 -3000 = 0
:
(r+60) *(r-50) = 0
:
r = -60 or 50, we reject the negative rate
:
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Jacqui's new speed is 50 + 10 = 60 mph
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