sondenso wrote:
Al, Pablo, and Marsha shared the driving on a 1,500-mile trip. Which of the three drove the greatest distance on the trip?
(1) Al drove 1 hour longer than Pablo but at an average rate of 5 miles per hour slower than Pablo.
(2) Marsha drove 9 hours and averaged 50 miles per hour.
We need to determine who (Al, Pablo and Marsha) drove the greatest distance of the 1,500-mile trip.
If we know one person had driven more than ½ the distance of the entire trip, i.e., 750 miles, then he or she must be the person who drove the greatest distance. On the other hand, if we know one person had driven less than ⅓ the distance of the entire trip, i.e., 500 miles, then he or she can’t be the person who dove the the greatest distance.
Statement One Alone:
Al drove 1 hour longer than Pablo but at an average rate of 5 miles per hour slower than Pablo.
Since we don’t know anything about Marsha, statement one alone is not sufficient to answer the question.
Statement Two Alone:
Marsha drove 9 hours and averaged 50 miles per hour.
We see that Marsha drove 9 x 50 = 450 miles. Since this is less than 500 miles, we know Marsha can’t be the person who drove the greatest distance. So either Al or Pablo is the person who drove the greatest distance. However, since we don’t know which one that is, statement two alone is not sufficient to answer the question.
Statements One and Two Together:
From the two statements, we see that Al and Pablo together drove 1,050 miles. If we let r = the average rate Al drove and t = the time he drove, we can create the equation:
rt + (r + 5)(t - 1) = 1,050
However, there are two unknowns in this equation, so we can’t determine who (Al or Pablo) drove a greater distance.
For example, suppose first that Al drove for 5 hours. Then, Pablo drove for 4 hours and we have
5r + 4(r + 5) = 1050
9r + 20 = 1050
9r = 1030
r ≈ 114 mph
Thus, Al drives approximately 5 x 114 = 570 miles and Pablo drives 1050 - 570 = 480 miles. In this scenario, Al drives further than Pablo.
On the other hand, suppose that Al drives for 15 hours. Then, Pablo drives for 14 hours and we have
15r + 14(r + 5) = 1050
29r + 70 = 1050
29r = 980
r ≈ 33 mph
Thus, Al drives approximately 15 x 33 = 495 miles and Pablo drives 555 miles. In this scenario, Pablo drives further than Al.
Answer: E
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