SOLUTION: Jacqui commutes 30 mi to her job each day. She finds that if she drives 10 mi/h faster, it takes her 6 min less to get to work. Find her new speed.
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Question 136647This question is from textbook Algebra Structure and Method
: Jacqui commutes 30 mi to her job each day. She finds that if she drives 10 mi/h faster, it takes her 6 min less to get to work. Find her new speed. This question is from textbook Algebra Structure and Method
You can put this solution on YOUR website! Jacqui commutes 30 mi to her job each day. She finds that if she drives 10 mi/h faster, it takes her 6 min less to get to work. Find her new speed
:
Let s = new speed
then
(s-10) = original speed
:
Convert 6 min to hrs: 6/60 = .1 hrs
:
Write a time equation: Time = dist/speed
:
Fast trip + 6 min = slow trip + .1 =
Multiply equation by s(s-10) to get rid of the denominators:
s(s-10)* + .1(s(s-10) = s(s-10)*
Results
30(s-10) + .1s^2 - 1s = 30s
:
30s - 300 + .1s^2 - s - 30s = 0
:
.1s^2 - s - 300 = 0; a quadratic equation
:
s^2 - 10s - 3000 = 0; mult by 10 to get rid of the decimal
Factors to:
(s-60)(s+50) = 0
:
S = 60 mph is the new speed
:
:
Check solution by finding the times of each trip:
30/50 = .6 hrs or 36 min
30/60 = .5 hrs or 30 min
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difference time = 6 min
