SOLUTION: this is a yes or no question..... A car travels a 1-mile track at an average speed of 15 mph. Is it possible for the car to travel the next mile so that the average speed for th

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Question 934569: this is a yes or no question.....
A car travels a 1-mile track at an average speed of 15 mph. Is it possible for the car to travel the next mile so that the average speed for the 2 mi is 30 mph?
thanks so much for the help!!
Found 3 solutions by josmiceli, jim_thompson5910, DrBeeee:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Average speed is always: ( total distance ) / ( total time )
The time for the 1st mile is: +1+%2F+15+ hrs
Let +t+ = the time for the 2nd mile in hrs
-----------------
You need to solve:
+30+=+%28+1+%2B+1+%29+%2F+%28+1%2F15+%2B+t+%29+
+30+=+2+%2F+%28+1%2F15+%2B+t+%29+
+1%2F15+%2B+t+=+2%2F30+
+1%2F15+%2B+t+=+1%2F15+
+t+=+1%2F15+-+1%2F15+
+t+=+0+
------------
It is impossible, since the car can't travel the 2nd
mile in zero time

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
A similar problem was asked/answered here

http://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.160404.html

The conclusion is that it is impossible to do so (the solver explains why). Let me know if that helps or not. Thanks.

Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Answer: No
Why, you ask?
Let's figure it out.
Let d = rt, with rate r in mph and t in hrs, then d is miles.
The time to travel the first mile is
(1) t1 = d/r or
(2) t1 = 1/15
Let the rate for the second mile be x, then the time for the second mile is
(3) t2 = 1/x
The average speed (rate) for the two miles is
(4) rave = d/t or
(5) rave = 2/(t1+t2) or
(6) rave = 2/(1/15 + 1/x)
We are asked if rave can be 30mph. Let's see. Can (6) be equal to 30?
(7) 30 = 2/(1/15 + 1/x) or
(8) 30 = 2/(x + 15)/(15x) or
(9) 30 = 30x/(x + 15) or
(10) 1 = x/(x + 15) or
(11) (x + 15) = x or
(12) 15 = 0
I don't recall that 15 = 0, do you?
So it is impossible. You need to travel the second mile in zero time. then we have in (5)
(13) rave = 2/(t1+t2) or
(14) rave = 2/(1/15+0) or
(15) rave = 2/(1/15) or
(16) rave = 30
It means that we travel at an infinite rate to take zero seconds!
You're welcome.