Question 455551
An aircraft travels at a speed of 550mph during the 1st half of it's journey and
 500mph during the second half of it's journey.
 Total flight time is 05:00 hours.
 Based on this determine the distance between the airport of departure and arrival." 
:
Let d = distance between the airports
:
Write a time equation: time = dist/speed
:
550mph time + 500mph time = 5 hrs
{{{(.5d)/550}}} + {{{(.5d)/500}}} = 5
multiply by 5500,
5500*{{{(.5d)/550}}} + 5500{{{(.5d)/500}}} = 5500(5)
cancel the denominators
10(.5d) + 11(.5d) = 27500
5d + 5.5d = 27500
10.5d = 27500
d = {{{27500/10.5}}}
d = 2619 mi
:
:
You can prove this to yourself, find the time at each speed
1309.5/550 = 2.38 hrs
1309.5/500 = 2.62 hrs
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total time:  5.0 hrs