ggarr wrote:
A cyclist rides his bicycle over a route which is 1/3 uphill, 1/3 level, and 1/3 downhill. If he covers the uphill part of the route at the rate of 16 miles per hour and the level part at the rate of 24 miles per hour, what rate in miles per hour would he have to travel the downhill part of the route in order to average 24 miles per hour for the entire route?
(A) 32
(B) 36
(C) 40
(D) 44
(E) 48
Please solve and explain why this doesn't this work:
1/3(16) + 1/3(24) + 1/3(x) = 24
And don't just give me your solution. Please let me know what's wrong w/the above. This equation was the first thing that came to my mind. I need to understand what I'm missing.
Please Show ALL work
Responding to a pm:
There are two problems with using the formula given on my blog on this question:
1. There are three different speeds which you need to average out.
2. The weights in case of speed is 'time taken' not distance traveled. (explained here:
bill-travels-first-40-of-the-distance-to-his-destination-at-137000.html#p1172411)
In case of three speeds, you can simply use the formula: Cavg = (C1*W1 + C2*W2 + C3*W3)/(W1 + W2 + W3)
Weight in case of speed is 'time taken'
Hence, Avg Speed = Total distance / Total time (which we know)
In this question, I would like to assume that the total distance is 48*3 such that the distance traveled in each leg of the journey uphill, level and downhill is 48 miles (you can assume it to be something else or x)
Time taken to go uphill = 48/16 = 3 hrs
Time taken on level = 48/24 = 2 hrs
Time taken to go downhill = 48/d
Avg Speed = 24 = 48*3/(3 + 2 + 48/d)
48/d = 1
d = 48 miles/hr
You can also look at it in another way - A Shortcut:
Speed on level plain is 24 miles/hr and average speed is also 24 miles/hr. So we can just ignore the level plain since it is at the average.
We need to average out the rest of the journey to 24 miles/hr. Again, assuming that distance of each leg is 48 miles,
24 = 48*2/(3 + 48/d)
d = 48 miles/hr
_________________
Karishma
Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >