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 2500 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 most appropriate option
A) 500  B) 625  C) 1,000  D) 1,500  E) 2,500
X13: (t, d, s)   Y14: (t, 3d, s+2500mi/hour)   Z15: (t+2 seconds, s, 5d)   d=?   Distance = Speed*Time   x13: d = s*t   x14: 3d = (s+2500)*t ===&gt; 3d = ts+2500t   z15: 5d = s*(t+2t) ===&gt; 5d = st+2st ===&gt; 5d - 2st = st   3d 5  - 2= 
<gadget id="calculator">5  - 2</gadget>
<output>3</output>
st   3d= 5d - 2st + 2500t   -2d = -2st + 2500t   2d = 2st - 2500t   d = st - 1250t   x13: d = s*t   st - 1250t = s*t   s - 1250 = s   -625 = s   I got to this point and couldn'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 Z15 is equal to five times the distance of X13 (we established that x13 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+2S = 5ST   T+2 = 5T   2=4T   t= 1/2   We are looking for distance (d=s*t) so we need to solve for speed now that we have time.   Speed y14 - speed x13   Speed = d/t   3d/t - d/t = 2500 (remember, t is the same because both asteroids were observed for the same amount of time)   2d = 2500   2 = 1250   d=s*t   d=1250*(1/2)= 
<gadget id="calculator">1250*(1/2)</gadget>
<output>625</output>
625   ANSWER: 625
<result>B</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 2500 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?