SOLUTION: driving 54 mph one covers 18 miles in how many seconds

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Question 472365: driving 54 mph one covers 18 miles in how many seconds
Found 2 solutions by Alan3354, richard1234:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
-sec%28t%29+-+1+=+%28sqrt%282%29+-+1%29%2Atan%28t%29
Multiply by cos(t)
-1+-+cos%28t%29+=+%28sqrt%282%29+-+1%29%2Asin%28t%29
cos%28t%29+%2B+1+=+%281+-+sqrt%282%29%29%2Asin%28t%29
sqrt%281+-+sin%5E2%28t%29%29+%2B+1+=+%281+-+sqrt%282%29%29%2Asin%28t%29
Sub x for sin(t)
sqrt%281+-+x%5E2%29+%2B+1+=+%281+-+sqrt%282%29%29%2Ax
sqrt%281+-+x%5E2%29+=+-1+%2B+%281+-+sqrt%282%29%29%2Ax
sqrt%281+-+x%5E2%29+=+-1+%2B+x+-+sqrt%282%29%2Ax
Square both sides
1+-+x%5E2+=+1+%2B+x%5E2+%2B+2x%5E2+%2B+2sqrt%282%29%2Ax+-+2sqrt%282%29%2Ax%5E2
0+=+x%5E2%2A%284+-+sqrt%288%29%29+%2B+2sqrt%282%29%2Ax
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x = 0, not allowed since sec(0) is undefined
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0+=+x%2A%284+-+sqrt%288%29%29+%2B+2sqrt%282%29
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x = 0 again --> no solution

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
18 miles is one third of 54 miles, so it will take 1/3 of an hour (we do not need to do much calculation in this case). 1/3 of an hour is equal to 20 minutes which is equal to 1200 seconds.