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The time it took car A to travel 400 miles was 2 hours less
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24 Apr 2020, 05:54
24 Apr 2020, 05:54
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The time it took car A to travel 400 miles was 2 hours less than the time it took car B to travel the same distance. If car A's average speed was 10 miles per hour greater than that of car B, what was car B's average speed in miles per hour?
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40
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Re: The time it took car A to travel 400 miles was 2 hours less
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24 Apr 2020, 07:30
24 Apr 2020, 07:30
Carcass wrote:
The time it took car A to travel 400 miles was 2 hours less than the time it took car B to travel the same distance. If car A's average speed was 10 miles per hour greater than that of car B, what was car B's average speed in miles per hour?
Show: :: OA
40
Car A's average speed was 10 miles per hour greater than that of car B
Let x = Car B's average speed
So, x + 10 = Car A's average speed
The time it took car A to travel 400 miles was 2 hours less than the time it took car B to travel the same distance
In other words: (car A's travel time) = (car B's travel time) - 2
time = distance/speed
So, we get: 400/(x + 10)) = 400/x - 2
Multiply both sides of the equation by (x + 10) to get: 400 = 400(x + 10)/x - (x + 10)(2)
Multiply both sides of the equation by x to get: 400x = 400(x + 10) - (x)(x + 10)(2)
Expand: 400x = 400x + 4000 - 2x² - 20x
Subtract 400x from both sides to get: 0 = 4000 - 2x² - 20x
Multiply both sides by -1 to get: 0 = -4000 + 2x² + 20x
Rewrite as follows: 2x² + 20x - 4000 = 0
Divide both sides by 2 to get: x² + 10x - 2000 = 0
Factor: (x + 50)(x - 40) = 0
So, EITHER x = -50 OR x = 40
Since the speed can't be negative, it must be the case that x = 40
Answer: 40
Cheers,
Brent
Re: The time it took car A to travel 400 miles was 2 hours less
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05 Jun 2023, 21:12
05 Jun 2023, 21:12
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Thanks to another GRE Prep 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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