SOLUTION: A train leaves Pittsburgh and travels 300 mi to Philadelphia. On the return trip, it travels 10 MPH faster. The total time for the round trip was 11 hrs. How fast did the train tra

Algebra ->  Test -> SOLUTION: A train leaves Pittsburgh and travels 300 mi to Philadelphia. On the return trip, it travels 10 MPH faster. The total time for the round trip was 11 hrs. How fast did the train tra      Log On


   

Question 628365: A train leaves Pittsburgh and travels 300 mi to Philadelphia. On the return trip, it travels 10 MPH faster. The total time for the round trip was 11 hrs. How fast did the train travel on each part?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A train leaves Pittsburgh and travels 300 mi to Philadelphia.
On the return trip, it travels 10 MPH faster.
The total time for the round trip was 11 hrs.
How fast did the train travel on each part?
:
Let s = speed on the initial trip
then
(s+10) = speed on the return trip
;
Write a time equation; time = dist/speed
:
300%2Fs + 300%2F%28%28s%2B10%29%29 = 11
Multiply by s(s+10), get rid of the denominators, results:
300(s+10) + 300s = 11s(s+10)
300s + 3000 + 300s = 11s^2 + 110s
a quadratic equation
0 = 11s^2 + 110s - 600s - 3000
11s^2 - 490s - 3000 = 0
You can use the quadratic equation, but this will factor:
(11s+60)(s-50) = 0
the positive solution is the only solution we want here
s = 50 mph on the initial trip
then
50 + 10 = 60 mph on the return trip
:
:
See if that checks out. Find the time of each trip.
300/50 = 6 hrs
300/60 = 5 hrs
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total hrs: 11