Al, Pablo and Marsha shared the driving on a 1,500-mile trip. Which of the three drove the greatest distance of 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.
The OA is E.
Please, can anyone explain this DS question? I'm not sure about it. I need help. Thanks.
Al, Pablo and Marsha shared the driving on a 1,500-mile trip
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Statement 1:swerve wrote:Al, Pablo and Marsha shared the driving on a 1,500-mile trip. Which of the three drove the greatest distance of 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.
No info about Martha.
INSUFFICIENT.
Statement 2:
Distance traveled by Martha = rt = 50*9 = 450 miles.
Remaining distance traveled by Al and Pablo = 1500 - 450 = 1050 miles.
Case 1: Al's distance = 1000 miles, Pablo's distance = 50 miles
In this case, Al drives the greatest distance.
Case 1: Al's distance = 50 miles, Pablo's distance = 1000 miles
In this case, Pablo drives the greatest distance.
INSUFFICIENT.
Statements combined:
Distance driven by Marsha = 50*9 = 450.
Distance traveled by Al and Pablo = 1500 - 450 = 1050.
Let the time for Pablo = t and the time for Al = t+1.
The rate for Pablo is 5mph greater than the rate for Al.
TEST EXTREME CASES.
Case 1: Rate for Pablo = 10mph, rate for Al = 5mph
Since the total distance driven by Pablo and Al is 1050, we get:
10t + 5(t+1) = 1050
15t = 1045
t = 1045/15 ≈ 70, implying that the time for Al ≈ 70+1 ≈ 71.
Distance for Pablo ≈ 10*70 ≈ 700, distance for Al ≈ 5*71 ≈ 355.
Pablo drives the greatest distance.
Case 2: Rate for Pablo = 1045mph, rate for Al = 1040mph
Since the total distance driven by Pablo and Al is 1050, we get:
1045t + 1040(t+1) = 1050.
2085t = 10
t = 10/2085 ≈ 1/200, implying that the time for Al ≈ 1/200 + 1 ≈ 201/200.
Distance for Pablo ≈ 1045(1/200) ≈ 5, distance for Al ≈ 1040(201/200) ≈ 1040.
Al drives the greatest distance.
Since in the first case Pablo drives the greatest distance, but in the second case Al drives the greatest distance, INSUFFICIENT.
The correct answer is E.
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We need to determine who (Al, Pablo and Marsha) drove the greatest distance of the 1,500-mile trip.swerve wrote:Al, Pablo and Marsha shared the driving on a 1,500-mile trip. Which of the three drove the greatest distance of 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.
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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