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rate problems : problem of my life

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rate problems : problem of my life

by NaimaB » Tue Dec 02, 2014 6:50 am
On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction of the total distance did he cover while the sun was shining on him?
(A)1/4
(B)4/5
(C)1/5
(D)1/6
(E)1/7

This math is from veritas prep practice test. I could not solve this one and i have noticed that i am facing problem regarding solving rate-distance related problems. I get confused from where to start solving this kind of problem. Even if i get clues and can solve, it takes long time. I seek help as i have my test in 2 weeks.

One more question, approx how many qs related to work rate and probability/combination usually come in the test?
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by GMATGuruNY » Tue Dec 02, 2014 7:00 am
On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction of the total distance did he cover while the sun was shining on him?

A. 1/4
B. 4/5
C. 1/5
D. 1/6
E. 1/7
The average speed -- 2.8 miles per hour -- must be BETWEEN the two individual rates (s and s+1).
Thus, s = 2 miles per hour and s+1 = 3 miles per hour.

We can treat this as a MIXTURE problem
A rate of 2 miles per hour is being combined with a rate of 3 miles per hour to yield an average speed of 2.8 miles per hour.
To determine how much WEIGHT must be given to each rate, we can use ALLIGATION:

Step 1: Plot the 3 rates on a number line, with the two individual rates (2 miles per hour and 3 miles per hour) on the ends and the average speed for the whole trip (2.8) in the middle.
2-------------------2.8-------------3

Step 2: Calculate the distances between the rates.
2--------0.8--------2.8------0.2-----3

Step 3: Determine the ratio of the rates.
The required ratio is the RECIPROCAL of the distances in red.
(2 miles per hour) : (3 miles per hour) = 0.2 : 0.8 = 1:4.

Here, the weight given to each rate is the amount of TIME spent at each rate.
The ratio above implies the following:
For every 1 hour spent traveling at 2 miles per hour, 4 hours must be spent traveling at 3 miles per hour.

Distance traveled in 1 hour at rate of 2 miles per hour = r*t = 2*1 = 2 miles.
Distance traveled in 4 hours at a rate of 3 miles per hour = r*t = 3*4 = 12 miles.
Of the total distance, the fraction traveled at 2 miles per hour = 2/(2+12) = 2/14 = 1/7.

The correct answer is E.
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by [email protected] » Tue Dec 02, 2014 11:06 am
Hi NaimaB,

It looks like this question was recently bumped up in another series of posts here:

https://www.beatthegmat.com/the-sun-was- ... 77335.html

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by NaimaB » Tue Dec 02, 2014 10:08 pm
Thanks to both of you.

Can anyone please comment on the rest part of my question?
This math is from veritas prep practice test. I could not solve this one and i have noticed that i am facing problem regarding solving rate-distance related problems. I get confused from where to start solving this kind of problem. Even if i get clues and can solve, it takes long time. I seek help as i have my test in 2 weeks.

One more question, approx how many qs related to work rate and probability/combination usually come in the test?
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by confused13 » Wed Dec 03, 2014 10:06 am
What is the difficulty level according to you experts?
I took 3 minutes to solve this question. Is this reasonable?
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by [email protected] » Wed Dec 03, 2014 6:30 pm
Hi confused13,

I imagine that it would take most Test Takers 2-3 minutes to answer this question. It's a wordy, weighted average prompt that involves 3 variables and a chunk of math is required, so if you spent 3 minutes solving it, then that's fine.

Here's an interesting follow-up question though: if something like this appeared on your next CAT, how quickly would you be able to solve THAT question? Would you recognize those patterns and connect them to what you did on this question? Part of your focus during your studies should be on building up your memory and pattern-recognition ability so that you can perform faster when similar-looking questions appear. This is one of many reasons why reviewing past work (not just the questions that you got wrong) can be beneficial to your long-term progress.

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