SOLUTION: A plane makes the trip from Acton to Banville at 800 km/h. The return, at 1000 km/h, takes 1/2 hour less than the initial flight. Find the distance between the towns.

Algebra ->  Algebra  -> Customizable Word Problem Solvers  -> Travel -> SOLUTION: A plane makes the trip from Acton to Banville at 800 km/h. The return, at 1000 km/h, takes 1/2 hour less than the initial flight. Find the distance between the towns.      Log On

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Question 555001: A plane makes the trip from Acton to Banville at 800 km/h. The return, at 1000 km/h, takes 1/2 hour less than the initial flight. Find the distance between the towns.
Answer by josmiceli(9697) About Me  (Show Source):
You can put this solution on YOUR website!
Let t = time in hours for 1st flight
Let d = distance between towns in km
Equation for A to B:
+d+=+800t+
Equation for B to A:
+d+=+1000%2A%28+t+-+1.5+%29+
----------------------------
Bt substitution:
+800t+=+1000t+-+1500+
+200t+=+1500+
+t+=+7.5+ hrs
and, since
+d+=+800t+
+d+=+800%2A7.5+
+d+=+6000+
The distance between the towns is 6,000 km
check:
+d+=+1000%2A%28+t+-+1.5+%29+
+d+=+1000%2A%28+7.5+-+1.5+%29+
+d+=+1000%2A6+
+d+=+6000+
OK