SOLUTION: On a sales trip, Gail drives the 600 miles to Richmond averaging a certain speed. The return trip is made at an average speed that is 10 mph slower. Total time for the round trip i

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: On a sales trip, Gail drives the 600 miles to Richmond averaging a certain speed. The return trip is made at an average speed that is 10 mph slower. Total time for the round trip i      Log On


   

Question 192618: On a sales trip, Gail drives the 600 miles to Richmond averaging a certain speed. The return trip is made at an average speed that is 10 mph slower. Total time for the round trip is 22 hours. Find Gail's average speed on each part of the trip.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let s= her average speed on the trip to Richmond
Let t%5B1%5D = time to get to Richmond
Let t%5B2%5D = time for return trip
given:
d+=+600 mi is the one-way distance
t%5B1%5D+%2B+t%5B2%5D+=+22 hr
-------------------
d+=+s%2At%5B1%5D
600+=+s%2At%5B1%5D
and
d+=+%28s+-+10%29%2A%2822+-+t%5B1%5D%29
600+=+%28s+-+10%29%2A%2822+-+t%5B1%5D%29
There are 2 equations with 2 unknowns, so it's solvable
600+=+22s+-+220+-+s%2At%5B1%5D+%2B+10t%5B1%5D
and, since 600+=+s%2At%5B1%5D,
600+=+22s+-+220+-+600+%2B+10t%5B1%5D
1420+=+22s+%2B+10%2A%28600%2Fs%29
1420s+=+22s%5E2+%2B+6000
22s%5E2+-+1420s+%2B+6000+=+0
11s%5E2+-+710s+%2B+3000+=+0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+11
b+=+-710
c+=+3000
x+=+%28-%28-710%29+%2B-+sqrt%28+%28-710%29%5E2-4%2A11%2A3000+%29%29%2F%282%2A11%29+
x+=+%28+710+%2B-+sqrt%28+504100-132000+%29%29%2F+22+
x+=+%28+710+%2B-+sqrt%28+372100+%29%29%2F+22+
x+=+%28+710+%2B-+610+%29%29%2F+22+
s+=+1320%2F22
s+=+60 mi/hr
s+-+10+=+50 mi/hr
the trip to Richmond was made at 60 mi/hr
The trip back at 50 mi/hr
check answer
600+=+%28s+-+10%29%2A%2822+-+t%5B1%5D%29
600+=+50%2A%2822+-+t%5B1%5D%29
600+=+1100+-+50t%5B1%5D
50t%5B1%5D+=+1100+-+600
50t%5B1%5D+=+500
t%5B1%5D+=+10 hr
t%5B2%5D+=+22+-+10
t%5B2%5D+=+12 hr
600+=+s%2At%5B1%5D
600+=+60%2A10
600+=+600
OK