SOLUTION: `A train goes from New Orleans to Boston at 40 mph. On the way back it returns with a speed of 80 miles per hour. If it takes one hour less time to return, what is it's average spe

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Question 980585: `A train goes from New Orleans to Boston at 40 mph. On the way back it returns with a speed of 80 miles per hour. If it takes one hour less time to return, what is it's average speed?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Average speed is always [ total distance ] / [ total time ]
Let +d+ = distance in miles between New Orleans and Boston
Let +t+ = time in hrs going from New Orleans to Boston
+t+-+1+ = time in hrs going from Boston to New Orleans
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Equation for New Orleans to Boston:
(1) +d+=+40t+
Equation for Boston to New Orleans:
(2) +d+=+80%2A%28+t-1+%29+
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[ total distance ] = +2d+
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(1) +t+=+d%2F40+
(2) +d+=+80%2A%28+t-1%29+
(2) +t-1+=+d%2F80+
---------------------------------
[ total time ] = +t+%2B+t-1+=+d%2F40+%2B+d%2F80+
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[ total distance ] / [ total time ] = +%28+2d+%29+%2F+%28+d%2F40+%2B+d%2F80+%29+
Divide top and bottom by +d+
+2+%2F+%28+1%2F40+%2B+1%2F80+%29+
Multiply top and bottom by +80+
+160+%2F+%28+2+%2B+1+%29+=+53.333+ mi/hr
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Note that you do not take the average of the two averages
which would be: +%28+40+%2B+80+%29+%2F+2+=+60+ mi/hr