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Jacob drove from Town A to Town B at an average rate of x miles per ho
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24 May 2021, 03:57
24 May 2021, 03:57
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Jacob drove from Town A to Town B at an average rate of x miles per hour, then returned along the same route at y miles per hour. If he then drove back to Town B at z miles per hour along the same route, what was Jacob’s average rate of speed for the entire trip, in miles per hour?
A. \(\frac{(x+y+z)}{3}\)
B. \(\frac{3xyz}{(xy+yz+zx)}\)
C. \(\frac{xyz}{(x+y+z)}\)
D. \(\frac{(xy+yz+zx)}{(x+y+z)}\)
E. \(\frac{3(x+y+z)}{xyz}\)
A. \(\frac{(x+y+z)}{3}\)
B. \(\frac{3xyz}{(xy+yz+zx)}\)
C. \(\frac{xyz}{(x+y+z)}\)
D. \(\frac{(xy+yz+zx)}{(x+y+z)}\)
E. \(\frac{3(x+y+z)}{xyz}\)
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Re: Jacob drove from Town A to Town B at an average rate of x miles per ho
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24 May 2021, 05:39
24 May 2021, 05:39
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Carcass wrote:
Jacob drove from Town A to Town B at an average rate of x miles per hour, then returned along the same route at y miles per hour. If he then drove back to Town B at z miles per hour along the same route, what was Jacob’s average rate of speed for the entire trip, in miles per hour?
A. \(\frac{(x+y+z)}{3}\)
B. \(\frac{3xyz}{(xy+yz+zx)}\)
C. \(\frac{xyz}{(x+y+z)}\)
D. \(\frac{(xy+yz+zx)}{(x+y+z)}\)
E. \(\frac{3(x+y+z)}{xyz}\)
A. \(\frac{(x+y+z)}{3}\)
B. \(\frac{3xyz}{(xy+yz+zx)}\)
C. \(\frac{xyz}{(x+y+z)}\)
D. \(\frac{(xy+yz+zx)}{(x+y+z)}\)
E. \(\frac{3(x+y+z)}{xyz}\)
Average speed = (total distance traveled)/(total travel time)
= (total distance)/(time of 1st journey + time of 2nd journey + time of 3rd journey)
Let d = the distance between Town A and Town B
So, total distance traveled = 3d
Time = distance/speed
time of 1st journey = d/x
time of 2nd journey = d/y
time of 3rd journey = d/z
Total time = d/x + d/y + dz
To simplify, rewrite with common denominator: dyz/xyz + dxz/xyz + dxy/xyz
So, total time = (dyz + dxz + dxy)/xyz
Average speed = (total distance)/(total time)
= 3d/[(dyz + dxz + dxy)/xyz]
= (3dxyz)/(dyz + dxz + dxy)
Divide top and bottom by d to get: (3xyz)/(yz + xz + xy)
Answer: B
Cheers,
Brent
gmatclubot
Re: Jacob drove from Town A to Town B at an average rate of x miles per ho [#permalink]
24 May 2021, 05:39
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