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 Post subject: GRE Speed / Distance / Time (Select One)
PostPosted: Fri Dec 10, 2010 6:37 am 
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Posts: 498
A bus traveled from its depot to its destination at an average speed of 60 kilometers per hour. On its return to the depot along the same route, the bus traveled at an average speed of only 40 kilometers per hour, making the trip 4 hours longer. What is the total distance of the round trip?

A. 360 kilometers
B. 400 kilometers
C. 600 kilometers
D. 800 kilometers
E. 960 kilometers

(E) The distance formula is Distance = Rate × Time. To solve this question, set x as the length of time (in hours) for the first trip. The distance to the destination city is 60 × x, where rate = 60 and time = x. The return trip was 4 hours longer, so its distance is 40(x + 4).

Since we know the distances are the same, we can set them equal to each other and solve for x:
60x = 40(x + 4)
60x = 40x + 160
20x = 160
x = 8.

So, the trip took 8 hours, and its distance is 8 × 60 = 480 kilometers. The question asks for the roundtrip distance, so we double the length of the one-way trip: 480 × 2 = 960 kilometers.

The correct answer is choice (E).


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 Post subject: Re: math: speed/distance/time
PostPosted: Fri Dec 10, 2010 6:54 am 
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There is an alternative way to solve this question. Unlike problems in reality, GRE gives you answer choices. That makes it possible to check those answer choices, rather than solve a problem itself.

You can do it by making a simple 4-columns table:
1st column - one way distance (half of the roundtrip)
2nd column - time in hours to travel one way at 60 km/hr (divide a number in column 1 by 60)
3rd column - number of hours to travel that same distance at 40 km/hr (divide a number in column 1 by 40)
4th column - difference between time in the second and in the third columns.


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 Post subject: Re: math: speed/distance/time
PostPosted: Fri Apr 22, 2011 5:11 pm 
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This question is not specific enough. 4 hours longer than what? ...than if he travelled at 60kil/hr the whole time? 4 hours longer on his trip back than his trip to?


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 Post subject: Re: math: speed/distance/time
PostPosted: Fri Apr 22, 2011 5:24 pm 
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Joined: Sun May 30, 2010 2:23 am
Posts: 498
There is only one value that comparison can refer to. This value is the duration of the trip from its depot to its destination, when the bus traveled at an average speed of 60 km/h.

So the bus went from the depot to some location at 60 km/h (an average speed).
Then it went from that location back to the depot along the same route at 40 km/h (an average speed).
The second trip took him 4 hours longer.

Note, that an average speed of 60 km/h does NOT mean that the bus traveled 60 km/h all the time. It could travel at various speed rates and even stop for some time, but nevertheless distance/time = average speed.


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