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

Question

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.

VenoMfTw · Accepted Answer

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

AryamaDuttaSaikia · Answer

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.

Hope this helps.

sb0541 · Answer

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 .

SamBoyle · Answer

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

gupta335 · Answer

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

Basshead · Answer

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

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