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A cyclist rode up and down a mountain along the same route each way. W

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RudeyboyZ
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A cyclist rode up and down a mountain along the same route each way. W [#permalink] New post   16 Aug 2015, 10:13
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A cyclist rode up and down a mountain along the same route each way. What was his average speed for the full trip?

(1) His uphill speed averaged 22 kilometers per hour, and his downhill speed averaged 48 kilometers per hour.

(2) The route is 16 kilometers each way.
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Re: A cyclist rode up and down a mountain along the same route each way. W [#permalink] New post   16 Aug 2015, 11:07
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RudeyboyZ wrote:
A cyclist rode up and down a mountain along the same route each way. What was his average speed for the full trip?

(1) His uphill speed averaged 22 kilometers per hour, and his downhill speed averaged 48 kilometers per hour.

(2) The route is 16 kilometers each way.


Avg Speed = \(\frac{Total distance}{Total Time}\)

Statement 1: His uphill speed averaged 22 kilometers per hour, and his downhill speed averaged 48 kilometers per hour.

Let "d' be the distance from starting point to the top of the mountain.
Total distance traveled = d+d= 2d
Total time = t1+t2 (t1 =time taken to ride up hill, t2 = time taken to ride down hill)

Avg speed = \(\frac{2d}{t1+t2}\)
time = \(\frac{distance}{speed}\)

Avg Speed =\(\frac{2d}{\frac{d}{22}+\frac{d}{48}}\)

Avg Speed =\(\frac{2}{\frac{1}{22}+\frac{1}{48}}\)

Thus we will end up with a unique value
Hence Sufficient


Statement 2: The route is 16 kilometers each way
Not suff
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Re: A cyclist rode up and down a mountain along the same route each way. W [#permalink] New post   17 Aug 2015, 12:12
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Average speed (scalar quantity) is calculated by finding the ratio of the "Total distance covered (irrespective of how the distance is covered) by the object / the time taken to cover that distance. Hope this answers your query.

Hope this helps.
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A cyclist rode up and down a mountain along the same route each way. [#permalink] New post   09 Feb 2017, 04:44
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A cyclist rode up and down a mountain along the same route each way. What was his average speed for the full trip?

(1) His uphill speed averaged 22 kilometers per hour, and his downhill speed averaged 48 kilometers per hour.

(2) The route is 16 kilometers each way.
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Re: A cyclist rode up and down a mountain along the same route each way. [#permalink] New post   09 Feb 2017, 10:46
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marcuccio wrote:
A cyclist rode up and down a mountain along the same route each way. What was his average speed for the full trip?

(1) His uphill speed averaged 22 kilometers per hour, and his downhill speed averaged 48 kilometers per hour.

(2) The route is 16 kilometers each way.


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Re: A cyclist rode up and down a mountain along the same route each way. W [#permalink] New post   21 Aug 2018, 08:41
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You can directly use the forumla - 2ab/(a+b) where a and b are the speeds and the distance is the same.

therefore, 1st statement is sufficient.

ans. A
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A cyclist rode up and down a mountain along the same route each way. W [#permalink] New post   16 Aug 2015, 11:30
but how do we know the exact degree of the angle of the uphill drive and downhill drive of the mountain? , what if the degree of angle was different for the uphill and downhill, for us to assume that both distances were equal wouldn't we also have to assume that the degree of angle was same for both, an assumption that goes beyond the understanding for a DS question in the GMAT. I hence clicked E. but the OA says A, am i missing something? can experts weigh in on this. Bunuel?
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Re: A cyclist rode up and down a mountain along the same route each way. [#permalink] New post   09 Feb 2017, 07:54
marcuccio wrote:
A cyclist rode up and down a mountain along the same route each way. What was his average speed for the full trip?

(1) His uphill speed averaged 22 kilometers per hour, and his downhill speed averaged 48 kilometers per hour.

(2) The route is 16 kilometers each way.



We can calculate Average speed by knowing the rate for up and down trip .
Statement 1 is sufficient .

22 Kms/ Hr --- 24 hrs -- 528 Kms
48 Kms / Hrs --- 11 hrs --- 528 kms

Total average is 1056 / 25 = 30.18 Kms/ hr

Answer is A .
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A cyclist rode up and down a mountain along the same route each way. W [#permalink] New post   07 Aug 2017, 14:21
We also can solve though not necessary here but good skills for other questions.

Quick trick to do 96 X 11 quickly or any number X 11. For instance 23 X 11 we do 2___3 and the middle number is adding 2+3 so 253

Or 43X11 is 4__3 and 4+3=7 so the answer is 473

Now 96 X 11 is 9___6 and 6+9=15 so the middle number is a 5 and we add the 1 to the 9 so 1056

97 X 11 is 9___7 and 9+7 =16 so the middle number is a 6 and add 1 to 9 so it is 1067.

A pretty cool math trick to help in computational speed
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Re: A cyclist rode up and down a mountain along the same route each way. W [#permalink] New post   13 Oct 2020, 05:48
We know the distance up and down the mountain is equal; thus, we can say the total distance is 2D.

average speed = 2D / t1 + t2

(1) Gives us the rate. From the rate we can determine the time it took to go up the mountain and the time it took to go down the mountain.

average speed = 1056 / 35 = 30.1 km/hr

(2) Not sufficient. Not able to determine the average speed with only the distance.
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Re: A cyclist rode up and down a mountain along the same route each way. W [#permalink] New post   15 Nov 2022, 00:21
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Re: A cyclist rode up and down a mountain along the same route each way. W [#permalink]
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