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I cover a total of 300 km in 8 hours, partly at a speed of 30 kmph and

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cfc198
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I cover a total of 300 km in 8 hours, partly at a speed of 30 kmph and [#permalink] New post   22 Apr 2019, 09:28
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I cover a total of 300 km in 8 hours, partly at a speed of 30 kmph and partly at a speed of 50
kmph. For what time was I traveling at a speed of 30 kmph?

1. 2 hrs
2. 3 hrs
3. 4 hrs
4. 5 hrs
5. 6 hrs
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D
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Re: I cover a total of 300 km in 8 hours, partly at a speed of 30 kmph and [#permalink] New post   22 Apr 2019, 09:44
Given that a total of 300 km is covered in 8 hours, partly at a speed of 30 kmph and partly at a speed of 50 kmph.

Let's assume that the time taken to cover the parts in 30 kmph and 50 kmph be x and y hours.
Therefore, 30x + 50y = 300
3x + 5y = 30...equation 1
Again, x + y = 8, i.e. y = 8 - x...equation 2
Subsitition equation 2 in equation 1: 30x + 50(8 - x) = 300
Solving for x, we get x = 5. Therefore, the time taken to travel in 30 kmph is 5 hours.

The correct answer is answer option D. 5 hours
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I cover a total of 300 km in 8 hours, partly at a speed of 30 kmph and [#permalink] New post   23 Apr 2019, 16:08
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Rate/Distance/Time problems were the most difficult for me to comprehend.

I've found using the table approach introduced in the GMATClub Math Book was the easiest way for me to develop a systematic approach to these questions



\(30x + 50(8-x) = 300\) , then solve
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Re: I cover a total of 300 km in 8 hours, partly at a speed of 30 kmph and [#permalink] New post   23 Apr 2019, 19:53
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cfc198 wrote:
I cover a total of 300 km in 8 hours, partly at a speed of 30 kmph and partly at a speed of 50
kmph. For what time was I traveling at a speed of 30 kmph?

1. 2 hrs
2. 3 hrs
3. 4 hrs
4. 5 hrs
5. 6 hrs


Let’s let t = the time spent traveling at 30 kmph. We can create the distance equation:

30t + 50(8 - t) = 300

30t + 400 - 50t = 300

-20t = -100

t = 5

So the time when I was traveling 30 kmph was 5 hours.

Answer: D/4
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Re: I cover a total of 300 km in 8 hours, partly at a speed of 30 kmph and [#permalink] New post   16 Dec 2023, 02:52
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: I cover a total of 300 km in 8 hours, partly at a speed of 30 kmph and [#permalink]
16 Dec 2023, 02:52
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