Jennifer drives 400 miles at a certain speed to New York Sta

Jennifer drives 400 miles at a certain speed to New York State for a ski vacation. When she returns home, the weather is bad and she drives 10 miles per hour slower and it takes her 2 hours longer. Find Jennifers speed on each part of the trip.

Solution

Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let r= her rate going to NY
Then r-10=her rate returning in the bad wx
Now we are told that her time coming back from NY is 2 hr longer than her time going, well:
Her time going to NY=400/r
Her time coming back=(400/(r-10)
Now if we subtract her time going from her time coming back we should have 2 hr.
So our equation to solve is:
400/(r-10) - 400/r=2 multiply each term by r(r-10)
400r-400r+4000=2r(r-10) simplify and divide each term by 2
2000=r^2-10r subtract 2000 from each side
r^2-10r-2000=2000-2000 collect like terms
r^2-10r-2000=0 quadratic in standard form and it can be factored
(r-50)(r+40)=0
Neglect the negative value for r. Rates in this problem are positive
r=50 mph---------------------------------- her rate going to NY
r-10=50-10=40 mph-----------------------her rate coming back from NY in the wx
CK
400/40 - 400/50=2
10-8=2
2=2