Hi,

Let r represent her old speed

d = r*t  

30 = r*t

30/r = t





Multiplying thru by 10r(r+10) so as all denominators = 1

300r = 300(r+10) - r(r+10)

300r = 300r + 3000 - r^ - 10r

r^2 + 10r - 3000 = 0

factor

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

x + 60)= 0  x = -60 cannot use

(x-50) = 0  x = 50mph her old speed.  Her new speed would be 60mph( 10mph faster) 

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
 Let r = original speed.





and let t = time to get to work driving that original speed.







So if "Liz commutes 30 mi. to her job each day", this means that  because we're using the formula  where the distance is 







So the first equation is 







In addition, because "she drives 10 mi/h faster it takes her 6 minutes less to get to work", we can say that 





Notes: since she drives 10 mph faster, her new speed is r+10. Also, because 60 min = 1 hour, this means that 6 min =  hours. So if it takes 6 mins or  or an hour less, then the new time is 







So the second equation is 







-----------------------------------------------------------





Now let's use both equations to solve for t and r







 Start with the first equation.







 Divide both sides by t to isolate r.







 Flip the equation.







 Move onto the second equation.







 Plug in 







 Multiply 10 by 







 Combine the fractions.







 Distribute







 Multiply.







Note: the 't' terms cancel in the first fraction while in the second, we're dividing each term by 10.







 Multiply EVERY term by the LCD 't' to clear out the fractions.







 Distribute.







 Subtract 30t from both sides.







 Combine like terms.









Notice that the quadratic  is in the form of  where , , and 







Let's use the quadratic formula to solve for "t":







 Start with the quadratic formula







 Plug in  , , and 







 Negate  to get . 







 Square  to get . 







 Multiply  to get 







 Rewrite  as 







 Add  to  to get 







 Multiply  and  to get . 







 Take the square root of  to get . 







 or  Break up the expression. 







 or  Combine like terms. 







 or  Simplify. 







So the possible solutions are  or  



  

  

However, since a negative time isn't possible, this means that the only solution for 't' is 







Remember that 't' is the time in hours. So convert to minutes to get  minutes







So the time it takes to travel 30 miles at the original speed is 36 minutes.







Recall that we made . So plug  into the equation to get 







So her original speed is 50 mph. Add 10 mph to this speed to get 50+10 = 60 mph







So her new speed is 60 mph.







I'll leave the check to you. Remember to use the formula 







If you need more help, email me at jim_thompson5910@hotmail.com





Also, feel free to check out my tutoring website





Jim 

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