SOLUTION: an airplane flew in a direct line from its base at the rate of 300 miles an hour and returned over the same route at the rate of 250 miles an hour, requiring 15 minutes longer on t

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Question 658752: an airplane flew in a direct line from its base at the rate of 300 miles an hour and returned over the same route at the rate of 250 miles an hour, requiring 15 minutes longer on the return trip. how far from its base did it fly?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time for 1st trip
Let +d+ = distance from base
Equation for 1st trip
(1) +d+=+300t+
Equation for 2nd trip:
(2) +d+=+250%2A%28+t+%2B+1%2F4+%29+
------------------------
Substitute (1) into (2)
(2) +300t+=+250%2A%28+t+%2B+1%2F4+%29+
(2) +300t+=+250t+%2B+250%2F4+
(2) +6t+=+5t+%2B+5%2F4+
(2) +t+=+5%2F4+
-------------
(1) +d+=+300%2A%285%2F4%29+
(1) +d+=+75%2A5+
(1) +d+=+375+
It flew 375 mi from base
check:
(2) +375+=+250%2A%28+t+%2B+1%2F4+%29+
(2) +3+=+2%2A%28+t+%2B+1%2F4+%29+
(2) +3+=+2t+%2B+1%2F2+
(2) +2t+=+5%2F2+
(2) +t+=+5%2F4+
OK