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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Joe regularly drives the 400 miles from A-ville to B-town at the same
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02 Feb 2022, 07:36
02 Feb 2022, 07:36
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Question Stats:
55% (02:08) correct
44% (03:29) wrong based on 9 sessions
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Joe regularly drives the 400 miles from A-ville to B-town at the same constant speed of r miles per hour. If Joe drives 30 mph faster than usual, it takes him 3 fewer hours to complete the trip. What is the value of r?
Show: ::
50
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Joe regularly drives the 400 miles from A-ville to B-town at the same
[#permalink]
06 Feb 2022, 07:50
06 Feb 2022, 07:50
1
GreenlightTestPrep wrote:
Joe regularly drives the 400 miles from A-ville to B-town at the same constant speed of r miles per hour. If Joe drives 30 mph faster than usual, it takes him 3 fewer hours to complete the trip. What is the value of r?
Show: ::
50
Let's start with a word equation.
In this question, we're comparing trips when Joe drives at his REGULAR speed with a HYPOTHETICAL trip at a faster speed
The question tells us that the HYPOTHETICAL trip takes 3 fewer hours than the REGULAR trip.
So, we can write: (time to complete REGULAR trip) - (time to complete HYPOTHETICAL trip) = 3 hours
If Joe's REGULAR speed is r miles per hour, then his HYPOTHETICAL speed must be r + 30
time = distance/speed
So we can substitute values into our word equation to get: 400/r - 400/(r + 30) = 3
Multiply both sides of the equation by r to get: 400 - 400r/(r+30) = 3r
Multiply both sides of the equation by r + 30 to get: 400(r + 30) - 400r = 3r(r+30)
Expand both sides: 400r + 12,000 - 400r = 3r² +90r
Simplify the left side: 12,000 = 3r² +90r
Subtract 12,000 from both sides: 0 = 3r² +90r - 12,000
Divide both sides by 3 to get: 0 = r² +30r - 4,000
Factor: 0 = (r + 80)(r - 50)
So, EITHER r = -80 OR r = 50
Since Bob's speed can't be negative, the correct answer is r = 50
Answer: 50
gmatclubot
Joe regularly drives the 400 miles from A-ville to B-town at the same [#permalink]
06 Feb 2022, 07:50
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