SOLUTION: OK guys this one is driving me nuts (as do all of them, but this one more most.) Here's what I've got: A jet flew at an average speed of 640 mph from LA to Chicago. Because of

Algebra ->  Human-and-algebraic-language -> SOLUTION: OK guys this one is driving me nuts (as do all of them, but this one more most.) Here's what I've got: A jet flew at an average speed of 640 mph from LA to Chicago. Because of      Log On


   

Question 262158: OK guys this one is driving me nuts (as do all of them, but this one more most.) Here's what I've got:
A jet flew at an average speed of 640 mph from LA to Chicago. Because of headwinds the jet averaged only 512 mph on the return trip, and took 48 minutes longer. How many hours was the flight from Chicago to LA? How far is Chicago to LA?
I swear I thought this was some kind of trick question. I've tried plugging those numbers in every which way but standing on my head, and I cannot build any kind of equation from them. It just seems like I'm a number short. Is there really enough information there to answer those questions?
Thanks!
Found 2 solutions by texttutoring, richwmiller:
Answer by texttutoring(324) About Me  (Show Source):
You can put this solution on YOUR website!
This problem involves the use of the equation d=vt, where d = distance, v = velocity and t = time.
Let d = the distance between Chicago and LA
v = 640mph
t = time of flight
d=vt
d=640%2At
On the return trip, the distance is the same, d, but it takes 48 minutes longer.
Convert 48 minutes to hours: 48/60 = 0.80 hours
the equation for the return trip is:
d = vt
d = (512)(t+0.8)
The two distances are the same (the original trip and the return trip) so we can just equate them:
d = d
640%2At+=+%28512%29%28t%2B0.8%29
640%2At+=+512%2At+%2B+512%2A0.8

Minus 512t from both sides:
128%2At+=+409.6

Divide both sides by 128:
+t+=+409.6%2F128
t+=+3.2+
So the time of the first trip is t=3.2 hours. The return trip takes 48 minutes (or 0.8 hours) longer.
t = 3.2 + 0.8
t = 4 hours
The return trip takes 4 hours.
We can then find the distance between Chicago and LA by using the d = vt equation:
d+=+640%2A3.2
d=2048
So the distance is d = 2048 miles.



Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
rt=d
rt=rt
640*(t-48/60)=512 *t
t=4 hours return trip Chicago to LA
512*4=2048 miles from Chicago to LA
Notice that i set it up so that t is the time from Chicago to LA and we don't even deal with the other time.