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Marcel is taking a trip, driving at a constant speed of X miles per ho
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01 Dec 2023, 12:30
01 Dec 2023, 12:30
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Data Insights (DI) Butler 2023-24 [Question #138, Date: Dec-01-2023] [Click here for Details]
Marcel is taking a trip, driving at a constant speed of X miles per hour for the first 2 hours of his trip, and at a constant speed of Y miles per hour after the first 2 hours.
In terms of X and Y, select the expression that represents Marcel’s average speed if he drives for a total of 5 hours, and select the expression that represents Marcel’s average speed if he drives for a total of 5X miles. Make only one selection in each column.
| Average speed over 5 hours | Average speed over 5X miles | |
| \(\frac{3Y}{5}\) | ||
| \(\frac{2X+3Y}{5}\) | ||
| \(\frac{3X-2Y}{5}\) | ||
| \(\frac{5XY}{2Y+3X}\) | ||
| \(\frac{5}{3Y}\) |
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Official Answer
Average speed over 5 hours: \(\frac{2X+3Y}{5}\)
Average speed over 5X miles: \(\frac{5XY}{2Y+3X}\)
GRE Forum Moderator
Joined: 02 Nov 2016
Posts: 14035
Given Kudos: 5807
GPA: 3.62
Re: Marcel is taking a trip, driving at a constant speed of X miles per ho
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11 Dec 2023, 23:20
11 Dec 2023, 23:20
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Official Explanation
The first question is easier to answer. If Marcel drives for 5 hours, then he goes at a constant speed of X for 2 hours and at a constant speed of Y for the remaining 3 hours. Thus, his average speed is \(\frac{2X+3Y}{5}\)
Now, if Marcel travels a total of 5X miles, then over the first 2 hours he covers 2X miles, so he has 3X miles left to travel at a speed of Y miles per hour:
\(\frac{Y miles}{1 hour}\) = \(\frac{3X miles}{?miles}\)
?=\(\frac{3X}{Y}\)
So he covers the remaining 3X miles in \(\frac{3X}{Y}\) hours. Therefore, in total his trip lasts \(2 + \frac{3X}{Y}\) hours. You can now find his average speed for the trip:
S = \(\frac{Total Distance}{Total Time}\)
S = \(\frac{5X}{2+(3X/Y)}\)
S = \(\frac{5X}{(2y+3X)/Y}\)
S = \(\frac{5XY}{2Y+3X}\)
The first question is easier to answer. If Marcel drives for 5 hours, then he goes at a constant speed of X for 2 hours and at a constant speed of Y for the remaining 3 hours. Thus, his average speed is \(\frac{2X+3Y}{5}\)
Now, if Marcel travels a total of 5X miles, then over the first 2 hours he covers 2X miles, so he has 3X miles left to travel at a speed of Y miles per hour:
\(\frac{Y miles}{1 hour}\) = \(\frac{3X miles}{?miles}\)
?=\(\frac{3X}{Y}\)
So he covers the remaining 3X miles in \(\frac{3X}{Y}\) hours. Therefore, in total his trip lasts \(2 + \frac{3X}{Y}\) hours. You can now find his average speed for the trip:
S = \(\frac{Total Distance}{Total Time}\)
S = \(\frac{5X}{2+(3X/Y)}\)
S = \(\frac{5X}{(2y+3X)/Y}\)
S = \(\frac{5XY}{2Y+3X}\)
General Discussion
Re: Marcel is taking a trip, driving at a constant speed of X miles per ho
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10 Dec 2023, 11:05
10 Dec 2023, 11:05
Can someone please tell me how did we get the answer to 'Average speed over 5 hours' problem?
