Question 1127986
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<pre>
From the condition, you have these two equations


v*(t+1.5) = 2700     (1)   ("the first plane flies 1.5 hours longer than the the second plane and travels 2700 miles")

v*t       = 2025     (2)   ("the second travels 2025 miles at the same rate")


where v is their <U>common</U> rate and t is flying time for the second plane.



Divide equation (1) by equation (2) (both sides.  You will get


{{{(t+1.5)/t}}} = {{{2700/2025}}} = {{{4/3}}}

3*(t+1.5) = 4t

3t + 4.5 = 4t

t = 4.5 hours.


<U>Answer</U>.  The second plane was flying for 4.5 hours;  the first plane was flying for  4.5 + 1.5 = 6 hours.
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Solved.


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This solution can be presented in wording form, with minimal use of equations.


<pre>
     The ratio of distances is  {{{2700/2025}}} = {{{4/3}}};  hence, the ratio of times is  {{{4/3}}}, too 
     (since the rate is the same for both planes).


    Hence, first plane traveled 4x hours, while the second plane traveled 3x hours.


    We are given that  4x - 3x  is  1.5 hours;  hence  x = 1.5 hours.

    Then the first plane was flying  4*1.5= 6 hours, while the second plane was flying 3*1.5 = 4.5 hours.


    You got the same answer.
</pre>

Solved for the second time.