Question 960908

Two planes make a 1000 mile flight, one flying 75 miles per hour faster than the other. The quicker plane makes the trip 3 hour faster. lHow long did it take the slower oplane to complete the flight?
<pre>Let time taken by slower plane be T
Then time taken by faster plane = T – 3
Speed of slower plane, equals speed of faster plane, less difference in speeds, OR
{{{1000/T = 1000/(T - 3) - 75}}}
1,000(T – 3) = 1,000T – 75T(T – 3) ------- Multiplying by LCD, T(T – 3)
{{{1000T - 3000 = 1000T - 75T^2 + 225T}}}
{{{75T^2 - 1000T - 225T + 1000T - 3000 = 0}}}
{{{75T^2 - 225T - 3000 = 0}}}
{{{75(T^2 - 3T - 40) = 75(0)}}}
{{{T^2 - 3T - 40 = 0}}}
(T - 8)(T + 5) = 0
T, or time taken by slower plane = {{{highlight_green(8)}}} hours		OR		T = - 5 (ignore)