SOLUTION: Question : A twin-engine plane can fly 800 mi in the same time that it takes a single-engine plane to fly 600 mi. The rate of the twin engine plane is 50 miles faster than that of

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Question 104935This question is from textbook
: Question : A twin-engine plane can fly 800 mi in the same time that it takes a single-engine plane to fly 600 mi. The rate of the twin engine plane is 50 miles faster than that of the single engine plane. Find the rate of the twin engine plane.
This is what I have tried:
distance/time=rate.
Twin engine 800 50+r
Single engine 600 50-r
So 800/50+r & 600/50-r
(50+r)(50-r)800/50+r=(50+r)(50-r)600/50-r
(50-r)800=(50+r)600
40000-800=30000+600
-1400=-10000
r=?
I have been trying to find wesites that could help me with this problem all week. The week for this problem is over tomorrow, October 18,2007, at 11:59pm.
Please help me ASAP! I have many other questions that need answering and I am looking forward to someone helping me out. This question is from textbook

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A twin-engine plane can fly 800 mi in the same time that it takes a single-engine plane to fly 600 mi. The rate of the twin engine plane is 50 miles faster than that of the single engine plane. Find the rate of the twin engine plane.
:
You got things a little mixed up here, here's how I would do it:
:
Let r = speed of the twin engine plane
then
(r-50) = speed of the single engine plane
:
The time of the two planes is given as the same so write a time equation:
Time = Distance/speed
:
Twin time = single time
800%2Fr = 600%2F%28r-50%29%29
Twin:
Cross multiply and you have:
800(r-50) = 600r
:
800r - 40000 = 600r; multiplied what's inside the brackets
:
800r - 600r = +40000
200r = 40000
r = 40000%2F200
r = 200 mph is the speed of the twin
:
:
WE can check our solutions by finding if the times are the same
Single plane speed is 200 - 50 = 150 mph
:
Twin: 800/200 = 4 hrs
Single: 600/150 = 4 hrs, confirms our solution:
:
Did that help? I think you made it more complicated than it is: