The speeds of three asteroids were compared. Asteroids X-13 and Y-14 w

Question

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 2000 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?

A. 500
B. 1,600/3
C. 1,000
D. 1,500
E. 2,500

A. 500
B. 1,600/3
C. 1,000
D. 1,500
E. 2,500

stne · Accepted Answer

Let distance of  (x-13 )  be  d  and time be  t . So speed of   x-13 = \frac{d}{t}

So distance of  (y-14 )  is  3d  and time is  t . So speed of   y-14 = \frac{3d}{t}

\frac{3d}{t} - \frac{d}{t} = 2000  .. (i)

Speed of  (z-15 ) = \frac{d}{t}

Distance travelled by  (z-15 )

= \frac{d}{t} * (t + 2 ) = 5d  .. (ii )

Solving (ii ) we get  t = \frac{1}{2}

Putting  t = \frac{1}{2}  in (i)

d= 500

Ans-A

Hope it's clear.

rahulms94 · Answer

E ???

This took me around 5 min+ to solve.

tx=ty=t sec (say)
dy=3dx -------(1) (given)
sy-sx =2000km/s ------(2) (given)

From (1),
sy*t = 3*sx*t
(2000+sx)*t = 3*sx*t
2000=2sx
 sx=1000km/s 
Therefore sy = 2000+1000=3000km/s.

Given
sz=sx = 1000km/s
tz = t+2 sec.

First we will find out how much distance was covered by z in the extra t+2 secs,
ie. dz = 1000*(t+2)km.

Also given that dz=5*dx
--> 1000(t+2) = 5*1000*t
Solving for t, we get t = 0.5s

therefore the distance covered by x, dx = 1000*0.5 = 500km.

Please feel free to correct me if I'm wrong. I took a while to get to this and I probably would still stump if I came across the exact same question again tomorrow.

RamseyGooner · Answer

We know time taken by x = y, so the distances and speeds are proportional.
Sx = x, Sy= 3x
3x-x = 2000
x = 1000km/s

Speed of X and Z is same, but as Z is observed for a longer time it travels 5 times as much distance as X

Mathematical translation :

Dx = D, Dz = 5D
Sz= Sx=x = 1000km/s
1000=D/t ------ For X
1000 = 5D/(t+2) ------ For Z

Solving, we get D = 500 which is (A)

Hope this helps!

800GMAT2019 · Answer

how long this take u guys? way to do to do it quicker?
any could do mentally? took me 5 min. on gmat for accuracy, i write out this type, but on real test 5 min on this too long.
shortcut way to write less without risking accuracy? TYSVM!

bumpbot · Answer

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The speeds of three asteroids were compared. Asteroids X-13 and Y-14 w

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