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
A bus trip of 450 miles would have taken 1 hour less if the
This topic has expert replies
-
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi All,
We're told that 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. We're asked for the average speed S, in miles per hour, for the trip. This question can be solved in a couple of different ways, including by TESTing THE ANSWERS.
To start, it's worth noting that increasing the speed by 5 miles/hour would decrease the travel time by EXACTLY 1 HOUR. This implies that the original speed and the increased speed are both factors of 450 (which is why the decrease in time is a nice 'round' number: 1 hour). Thus, we should look to TEST the answers that are divisors of 450. Let's TEST Answer D first...
Answer D: 50 miles/hour
At 50 miles/hour, the trip would take 450/50 = 9 hours
At 55 miles/hour, the trip would take 450/55 = something between 8 hours and 9 hours. This would NOT lead to a difference of 1 hour (and notice how 55 is NOT a divisor of 450). However, 45 IS a divisor.... so let's TEST answer C next...
Answer C: 45 miles/hour
At 45 miles/hour, the trip would take 450/45 = 10 hours
At 50 miles/hour, the trip would take 450/50 = 9 hours
This is an exact different of 1 hour, so this must be the answer.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
We're told that 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. We're asked for the average speed S, in miles per hour, for the trip. This question can be solved in a couple of different ways, including by TESTing THE ANSWERS.
To start, it's worth noting that increasing the speed by 5 miles/hour would decrease the travel time by EXACTLY 1 HOUR. This implies that the original speed and the increased speed are both factors of 450 (which is why the decrease in time is a nice 'round' number: 1 hour). Thus, we should look to TEST the answers that are divisors of 450. Let's TEST Answer D first...
Answer D: 50 miles/hour
At 50 miles/hour, the trip would take 450/50 = 9 hours
At 55 miles/hour, the trip would take 450/55 = something between 8 hours and 9 hours. This would NOT lead to a difference of 1 hour (and notice how 55 is NOT a divisor of 450). However, 45 IS a divisor.... so let's TEST answer C next...
Answer C: 45 miles/hour
At 45 miles/hour, the trip would take 450/45 = 10 hours
At 50 miles/hour, the trip would take 450/50 = 9 hours
This is an exact different of 1 hour, so this must be the answer.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Since the time difference yielded by the two speeds is an INTEGER -- 1 hour less -- the actual speed and hypothetical greater speed must both divide evenly into the 450-mile distance.BTGmoderatorDC 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
We can PLUG IN THE ANSWERS, which represent the actual speed.
Since A, B and E do not evenly into 450, eliminate A, B and E.
The hypothetical greater speed is 5 miles per hour greater than the actual speed.
D implies that the hypothetical greater speed = 50+5 = 55.
Since 55 does not divide evenly into 450, eliminate D.
The correct answer is C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Let's start with a word equation:BTGmoderatorDC 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
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
GMAT/MBA Expert
- Jeff@TargetTestPrep
- GMAT Instructor
- Posts: 1462
- Joined: Thu Apr 09, 2015 9:34 am
- Location: New York, NY
- Thanked: 39 times
- Followed by:22 members
Let t = the time to complete the trip of 450 miles when the average speed is S. Thus, we have:BTGmoderatorDC 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
St = 450
and
(S + 5)(t - 1) = 450
Isolating t in the first equation, we have: t = 450/S. Substituting this in the second equation, we have:
(S + 5)(450/S - 1) = 450
450 - S + 2250/S - 5 = 450
-S + 2250/S - 5 = 0
S + 5 - 2250/S = 0
S^2 + 5S - 2250 = 0
(S + 50)(S - 45) = 0
S = -50 or S = 45
Since S can't be negative, S = 45.
Answer: C
Jeffrey Miller
Head of GMAT Instruction
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews