SOLUTION: Helena drives from town A to town B at x mph, and drives back at y mph. What is her average speed for the round trip? If the round trip takes t hours, how far apart are the towns?

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Helena drives from town A to town B at x mph, and drives back at y mph. What is her average speed for the round trip? If the round trip takes t hours, how far apart are the towns?      Log On

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Question 570740: Helena drives from town A to town B at x mph, and drives back at y mph. What is her average speed for the round trip? If the round trip takes t hours, how far apart are the towns?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Average speed is always ( total distance traveled ) / ( total time it takes )
I will say that the towns are +d+ miles apart
----------
Time going from A to B:
+d%2Fx+
Time going from B to A:
+d%2Fy+
----------
Ave speed = +%282d%29+%2F+%28+d%2Fx+%2B+d%2Fy+%29+
Divide top and bottom by d
Ave speed = +2+%2F+%28+1%2Fx+%2B+1%2Fy+%29+
Multiply top and bottom by +x%2Ay+
Ave speed = +%282%2Ax%2Ay%29+%2F+%28+x+%2B+y+%29+
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If the round trip takes +t+ hrs,
+%282d%29%2Ft+=+%282%2Ax%2Ay%29+%2F+%28+x+%2B+y+%29+
Distance apart is +d+=+%28x%2Ay%2At%29+%2F+%28+x+%2B+y+%29+