You may have noticed on the GMAC official Integrated Reasoning practice questions for Two-Part Analysis that rates and work have appeared as a tested concept. While rates and work already appear on the GMAT’s Quantitative section, it’s logical to assume that they will also continue to make an appearance on the new IR section once it fully launches in June 2012. In the meantime, let’s review the first of two necessary formulas to approach this type of concept:
D = R x T
This stands for Distance = Rate x Time. It is perfectly acceptable to also think of it as Time = Distance / Rate or as Rate = Distance / Time. In a Two-Part Analysis question, if you see the word “per” you know this is a question involving rates. The second formula is: Average Rate = Total Distance / Total Time. Let’s try a practice question that is more like a classic Quantitative word problem.
Question 1: Cindy spent all day on a sightseeing tour in France. First she boarded the bus which went 15mph through a 30 mile section of the countryside. The bus then stopped for lunch in Paris before continuing on a 3 hour tour of the city’s sights at speed of 10mph. Finally, the bus left the city and drove 40 miles straight back to the hotel. Marion arrived back at her hotel exactly 2 hours after leaving Paris. What was the bus’s average rate for the entire journey?
For the first part of the trip, we know that 30 miles = 15mph x T, so we know that T = 2 hours. For the middle part of the trip, we know that D = 10mph x 3 hours, so we know that D = 30 miles. For the last part of the trip, we know that 40 miles = R x 2 hours, so we know that R = 20mph. Now we can find the Total Distance and the Total Time. Total Distance = 30 miles + 30 miles + 40miles = 100 miles. Total Time = 2 hours + 3 hours + 2 hours = 7 hours. So the Average Rate = 100 miles/ 7 hours = 14.28mph.
Now, let’s look at a practice Grockit Two-Part Analysis question involving Rates and Work!
Question 2: Set On You Concrete is considering buying two new cement mixes for its popular patio tiles, Stone Ground and Ready to Rock. The company buys its cement mixes by the pound and pays $1 per pound per minute to mix it into cement. Stone Ground costs $6 per pound and takes 10 minutes to mix, while Ready to Rock costs $7 per pound and takes an unknown time to mix.
Identify the costs (rounded to the nearest dollar) of cement of each type that could be mixed completely in an hour on its own in a 50-pound mixer, if Ready To Rock’s average cost per pound per minute of mixing is 90% of Stone Ground’s.
Stone Ground Ready To Rock
Stone Ground costs $6 per pound, and costs $10 per pound to mix, for a total of $16/10 minutes, or $1.60/minute in 10-minute intervals. There would be 6 full intervals in an hour, so a 50-pound mixer would roast (50 pounds * 6 intervals* 10 minutes * $1.60 per minute per pound =) $4800 of cement.
Ready To Rock costs $7/pound, and has 90% the cost per minute of mixing, so its cost is $1.44/minute, and if x = the number of minutes of mixing:
(7 +x)/x= 1.44
x+7 = 1.44x
.44x = 7
Ready To Rock mixes for 15.9 minutes at an average of $1.44/minute. There would be 3 full 15-minute intervals in an hour, so a 50-pound mixer would roast (50 pounds * 3 intervals* 15.9 minutes * $1.44 per minute per pound =) $3434 of cement.
Answer: $4800; $3434
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