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

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
------------------------
Old DATA:
distance = 30 miles ; rate = x mph ; time = d/r = 30/x hrs.
--------------------------------------------------
New DATA:
distance = 30 miles ; rate = (x+10) mph ; time = d/r = 30/(x+10) hrs
------------------------------------------------------
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
---
Positive solution:
x = 50 mph (old speed)
---
x+10 = 60 mph (her new speed)
==================================
Cheers,
Stan H.
RELATED QUESTIONS
Jacqui commutes 30 mi to her job each day. She finds that if she drives 10 mi/h faster,... (answered by ankor@dixie-net.com)
Jacqui commutes 30 mi to her job each day. She finds that if she drives 10 mi/h faster,... (answered by ankor@dixie-net.com)
Liz commutes 30 mi. to her job each day. She finds that if she drives 10 mi/h faster it... (answered by mananth)
Jacqui commutes 30 mi to her job each day.She finds that if she drives 10mi/faster, it... (answered by josgarithmetic,MathTherapy,rothauserc)
Liz commutes 30 mi. to her job each day. She Finds that if she drives 10 mi/h faster it... (answered by ewatrrr,jim_thompson5910)
Nancy drives 20 miles to her school each day. If she drives 10 miles per hour faster, it... (answered by richwmiller)
Cindy drives 10 miles to school. If she drives 30 miles per hour the entire way to... (answered by ikleyn)
A girl walks 1.25 miles a hour and to get to her destination it takes 1 hour and 30 mins. (answered by LinnW)
A woman drives 10 miles, then increases her speed by 10 miles per hour and drives 25... (answered by fractalier)