document.write( "Question 766914: Airplane A travels 1400km at a certain speed. Plane B travels 1000km at a speed 50 km/h faster than plane A in 3 hrs less time. Find the same speed of each plane. \n" ); document.write( "

Algebra.Com's Answer #467319 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

You can put this solution on YOUR website!
Airplane A travels 1400km at a certain speed.
\n" ); document.write( " Plane B travels 1000km at a speed 50 km/h faster than plane A in 3 hrs less time.
\n" ); document.write( "Find the same speed of each plane.
\n" ); document.write( ":
\n" ); document.write( "let s = Plane A's speed
\n" ); document.write( "then
\n" ); document.write( "(s+50) = B's speed
\n" ); document.write( ":
\n" ); document.write( "Write a time equation; time = dist/speed
\n" ); document.write( ":
\n" ); document.write( "A's time - B's time = 3 hrs
\n" ); document.write( " $\"1400%2Fs\"$ - $\"1000%2F%28%28s%2B50%29%29\"$ = 3
\n" ); document.write( "multiply by s(s+50), resulting in:
\n" ); document.write( "1400(s+50) - 1000s = 3s(s+50)
\n" ); document.write( "1400s + 70000 - 1000s = 3s^2 + 150s
\n" ); document.write( "Combine to form a quadratic equation on the right
\n" ); document.write( "0 = 3s^2 + 150s - 400s - 70000
\n" ); document.write( "3s^2 - 250s - 70000
\n" ); document.write( "Factors to
\n" ); document.write( "(3s + 350)(s - 200)
\n" ); document.write( "We only want the positive solution here
\n" ); document.write( "s = 200 mph is the speed of A
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check this, find the time of each plane
\n" ); document.write( "1400/200 = 7 hrs
\n" ); document.write( "1000/250 = 4 hrs
\n" ); document.write( "------------------
\n" ); document.write( "time dif: 3 hrs \n" ); document.write( "

\n" );