the speeds of three asteroids were compared. asteroids x - 13 and y - 14 were observed for identical durations, while asteroid z - 15 was observed for 2 seconds longer. during its period of observation, asteroid y - 14 traveled three times the distance x - 13 traveled, and therefore y - 14 was found to be faster than x - 13 by 1000 kilometers per second. asteroid z - 15 had an identical speed as that of x - 13, but because z - 15 was observed for a longer period, it traveled five times the distance x - 13 traveled during x - 13 ' s inspection. asteroid x - 13 traveled how many kilometers during its observation? Choose the correct choice from the following answers:	A) 250	B) 1,600 / 3	C) 1,000	D) 1,500	E) 2,500
<gadget id="calculator">1_000 / 2</gadget>
<output>500</output>

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">500 * (1/2)</gadget>
<output>250</output>

<result>A</result>
the speeds of three asteroids were compared. asteroids x - 13 and y - 14 were observed for identical durations, while asteroid z - 15 was observed for 2 seconds longer. during its period of observation, asteroid y - 14 traveled three times the distance x - 13 traveled, and therefore y - 14 was found to be faster than x - 13 by 1000 kilometers per second. asteroid z - 15 had an identical speed as that of x - 13, but because z - 15 was observed for a longer period, it traveled five times the distance x - 13 traveled during x - 13 ' s inspection. asteroid x - 13 traveled how many kilometers during its observation?
multiply(divide(1000, 2), divide(const_1, 2))
"x 13 : ( t , d , s ) y 14 : ( t , 3 d , s + 1000 mi / hour ) z 15 : ( t + 2 seconds , s , 5 d ) d = ? distance = speed * time x 13 : d = s * t x 14 : 3 d = ( s + 1000 ) * t = = = > 3 d = ts + 1000 t z 15 : 5 d = s * ( t + 2 t ) = = = > 5 d = st + 2 st = = = > 5 d - 2 st = st 3 d = 5 d - 2 st + 1000 t - 2 d = - 2 st + 1000 t 2 d = 2 st - 1000 t d = st - 500 t x 13 : d = s * t st - 500 t = s * t s - 500 = s - 250 = s i got to this point and could n ' t go any further . this seems like a problem where i can set up individual d = r * t formulas and solve but it appears that ' s not the case . for future reference how would i know not to waste my time setting up this problem in the aforementioned way ? thanks ! ! ! the distance of z 15 is equal to five times the distance of x 13 ( we established that x 13 is the baseline and thus , it ' s measurements are d , s , t ) s ( t + 2 ) = 5 ( s * t ) what clues would i have to know to set up the equation in this fashion ? is it because i am better off setting two identical distances together ? st + 2 s = 5 st t + 2 = 5 t 2 = 4 t t = 1 / 2 we are looking for distance ( d = s * t ) so we need to solve for speed now that we have time . speed y 14 - speed x 13 speed = d / t 3 d / t - d / t = 1000 ( remember , t is the same because both asteroids were observed for the same amount of time ) 2 d = 1000 2 = 500 d = s * t d = 500 * ( 1 / 2 ) d = 250 answer : a"