In a trolley ride around an amusement park, a child traveled from one signpost to a second signpost at a constant speed of 125 meters per minute. Was the distance that the child traveled from the first signpost to the second signpost greater than 0.8 kilometer? (1 kilometer = 1,000 meters) (1) It took less than 450 seconds for the child to travel from the first signpost to the second signpost. (2) It took more than 400 seconds for the child to travel from the first signpost to the second signpost.

Answer:Given speed of trolley = 125 meters per minute[tex]Speed= 125 meters/minute\\\\Speed =\frac{125}{60}meters/second\\\\Speed=2.083m/s[/tex]Now we know thatDistance= Speed x timeThus for the first case since the time of travel is less than 450 seconds thus the distance traveled is less thanDistance < 2.083 x 450 =937.5 metershence depending on the given information we cannot come to any conclusion weather the distance travelled is less than 800 m or greater than 800 m.For the second case since the time of travel is greater than 400 secondsThus the distance traveled is [tex]Distance>2.083\times 400=833.2meters[/tex]which is greater than 800 meters.