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?

Question

Yaretzi Osborn

Mathematics

27 June, 06:58

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?

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Felicity Jacobson · Answer 1

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)