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A bus trip of 450 miles would have taken 1 hour less if the average sp
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28 Apr 2021, 08:38
28 Apr 2021, 08:38
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A bus trip of 450 miles would have taken 1 hour less if the average speed S for the trip had been greater by 5 miles per hour. What was the average speed S, in miles per hour, for the trip?
(A) 10
(B) 40
(C) 45
(D) 50
(E) 55
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
(A) 10
(B) 40
(C) 45
(D) 50
(E) 55
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Joined: 10 Apr 2015
Posts: 6218
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Re: A bus trip of 450 miles would have taken 1 hour less if the average sp
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28 Apr 2021, 08:47
28 Apr 2021, 08:47
1
Carcass wrote:
A bus trip of 450 miles would have taken 1 hour less if the average speed S for the trip had been greater by 5 miles per hour. What was the average speed S, in miles per hour, for the trip?
(A) 10
(B) 40
(C) 45
(D) 50
(E) 55
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
(A) 10
(B) 40
(C) 45
(D) 50
(E) 55
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Let's start with a word equation:
travel time at actual speed = travel time at faster speed + 1 hour
In other words: travel time at S mph = travel time at (S + 5) mph + 1 hour
travel time = distance/speed
So, we get: 450/S= 450/(S + 5) + 1
Multiply both sides by S to get: 450 = 450S/(S+5) + S
Multiply both sides by S+5 to get: 450(S + 5) = 450S + S(S+5)
Expand: 450S + 2250 = 450S + S² + 5S
Subtract 450S from both sides: 2250 = S² + 5S
Rewrite as: S² + 5S - 2250 = 0
Factor: (S + 50)(S - 45) = 0
So, EITHER S = 50, OR S = 45
Since the speed can't be negative, the correct answer must be S = 45
Answer: C
Cheers,
Brent
gmatclubot
Re: A bus trip of 450 miles would have taken 1 hour less if the average sp [#permalink]
28 Apr 2021, 08:47
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