# 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 Answer by ankor@dixie-net.com(15633)   (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 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 ------------------------ difference time = 6 min =