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Question
John met some aliens, Arnax, Thorinax and Glorfmorax, each possessing their own spaceship. Arnax had 2 times as many batteries as Thorinax, but 20 batteries less than Glorfmorax. Glorfmorax has 22 batteries more than Thorax.
Each battery ups the speed of their spaceship by 1000 mph. Now assume that no acceleration is required to obtain this speed. The 3 aliens, currently on the same location, are racing to the planet Durinorax, which is located twice as far as Curnorax, yet 300 miles closer than Smurnorax. Once Arnax reaches Curnorax, Glorfmorax would have to travel 50 more miles to go twice as far as the planet Smurnorax.
Once Glorfmorax has reached Curnorax, how much longer would it take for Thorinax to reach Smurnorax? Please give your answer in seconds!
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Hmm, somehow I don't get sensible results.
Glorfmorax has 24 batteries, Thorinax has 2 and Arnax 4.
Durinorax is located twice as far as Curnorax: D=2xC
Durinorax is 300 miles closer than Smurnorax: D=S-300
Once Arnax reaches Curnorax, Glorfmorax would have to travel 50 more miles to go twice as far as the planet Smurnorax:
AxC=G(2xS-50)
where A and G are the speed in batteries times 1000mph.
Inserting the three equations into each other gives for the distance to Smurnorax of s=13.0434782609 miles. This makes the distances to Curnorax and Durinorax negative!
Don't know if I or you made a mistake. Anyway fun idea. I like it!
Could you try using 3x3 instead of 3*3? That reason for this is that the latter one makes it CURSIVE instead of showing it. That may make it easier to understand your concerns...
And yes, the battery part is correct. I think you should redo the 2nd part with the x's instead of *'s though... Then I might be able to help.
I tried solving it myself and got it correct, but I might just be repeating the same mistake :P
There you go. Updated it.
My reasoning is that from the first two equations I get a relation between the distance to Curnorax and the distance to Smurnorax. C and S standing for the respective distances, I get: C=S/2-150.
Inserting that into my third equation I get:
A(S/2-150)=G(2xS-50) which yields the S of my previous post, which is too small.
You made a little mistake... Why would you multiply the speed by the respective distances?
If you multiply speed by distance, you get... well... it's nothing measurable really.. You have to divide the distance by the speed to obtain the time it takes to reach certain places. From there you can easily derive the distances. So try dividing instead of multiplying.
I tried to solve it again and succesfully obtained the same answer as I had obtained the first time I tested it. Good Luck if you're still interested :P
Uhh, that was quite a stupid mistake. If I didn't make another one, I get that Thorinax reaches Smurnorax 1496.25 seconds after Glorfmorax has reached Curnorax.
If this is not correct I'm done. :-)
Yeah, that's correct :)
413.54166... seconds
Incorrect, but nice attempt. Atleast you're in the same order of magnitude.
My first try was way off.
But now I get 1488.75 seconds
T = 2000 mph
A = 4000 mph
G = 24,000 mph
S = 2C + 300 miles
time for A to go to C = time for G to go to 2 S - 50 =
C/A = (2 S - 50)/G
S = 3C + 25 miles
C = 275 miles
D = 550 miles
S = 850 miles
time for T to go to S = S/T = (850/2000)3600 sec = 1530 sec
time for G to go to C = C/G = (275/24,000)3600 sec = 41.25 sec
1530 sec - 41.25 sec = 1488.75 sec.
Correct! 1488.75 is the right answer! :)
Well done.. :D