Last visit was: 21 Dec 2024, 06:15 It is currently 21 Dec 2024, 06:15
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

Close

GRE Prep Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GRE score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
PREVIOUS TOPIC
NEXT TOPIC

Two people walk the same distance of 15miles, in which A spends 15 min

Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

avatar
S
COolguy101
Senior Manager
Senior Manager
Joined: 23 Jan 2021
Posts: 294
Own Kudos [?]: 172 [2]
Given Kudos: 81
Concentration: , International Business
Send PM
Two people walk the same distance of 15miles, in which A spends 15 min [#permalink] New post   12 Aug 2021, 19:34
2
Bookmarks
00:00

Question Stats:

33% (01:07) correct 66% (03:09) wrong based on 6 sessions

Hide Show timer Statistics

Two people walk the same distance of 15 miles, in which A spends 15 minutes less than B, and the speed of B is 10 miles/h slower than the speed of A. What is the speed of B?


Show: :: OA
\(20\)
Most Helpful Community Reply
User avatar
D
KarunMendiratta
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Own Kudos [?]: 3259 [1]
Given Kudos: 172
Location: India
WE:Education (Education)
Send PM
Re: Two people walk the same distance of 15miles, in which A spends 15 min [#permalink] New post   13 Aug 2021, 08:05
1
COolguy101 wrote:
COolguy101 wrote:
Two people walk the same distance of 15 miles, in which A spends 15 minutes less than B, and the speed of B is 10 miles/h slower than the speed of A. What is the speed of B?


Show: :: OA
\(20\)



GreenlightTestPrep KarunMendiratta rx10 sir, please help me .


Let,
D be the distance
T be the time
and S be speed

Given:
\(D_A = D_B = 15\)
\(T_A = T_B - \frac{15}{60}\)
\(S_A = S_B + 10\)

\(T_A = T_B - \frac{15}{60}\)

\(\frac{15}{S_B + 10} = \frac{15}{S_B} - \frac{15}{60}\)

\(\frac{15}{S_B} - \frac{15}{S_B + 10} = \frac{15}{60}\)

\(\frac{15(S_B + 10) - 15(S_B)}{S_B(S_B + 10)} = \frac{1}{4}\)

\((15S_B + 150 - 15S_B)(4) = S_B^2 + 10S_B\)

\(S_B^2 + 10S_B - 600 = 0\)

Solve for \(S_B = 20\)
General Discussion
avatar
S
COolguy101
Senior Manager
Senior Manager
Joined: 23 Jan 2021
Posts: 294
Own Kudos [?]: 172 [0]
Given Kudos: 81
Concentration: , International Business
Send PM
Re: Two people walk the same distance of 15miles, in which A spends 15 min [#permalink] New post   13 Aug 2021, 06:52
COolguy101 wrote:
Two people walk the same distance of 15 miles, in which A spends 15 minutes less than B, and the speed of B is 10 miles/h slower than the speed of A. What is the speed of B?


Show: :: OA
\(20\)



GreenlightTestPrep KarunMendiratta rx10 sir, please help me .
User avatar
P
GreenlightTestPrep
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12231 [2]
Given Kudos: 136
Send PM

Top Member of the Month
Re: Two people walk the same distance of 15miles, in which A spends 15 min [#permalink] New post   13 Aug 2021, 07:12
2
COolguy101 wrote:
Two people walk the same distance of 15 miles, in which A spends 15 minutes less than B, and the speed of B is 10 miles/h slower than the speed of A. What is the speed of B?
Show: :: OA
\(20\)


The speed of B is 10 miles/h slower than the speed of A
Let x = B's speed (in miles per hour)
So, x + 10 = A's speed (in miles per hour)

A spends 15 minutes less than B
Time = distance/rate
So, B's travel time = 15/x
And A's travel time = 15/(x + 10)

Since we're dealing with rates measured in miles per HOUR, will convert 15 minutes to 0.25 HOURS
We can write: (A's travel time) = (B's travel time) - 0.25
Substitute to get: 15/(x + 10) = 15/x - 0.25

To solve for x, will first multiply both sides of the equation by (x + 10) to get: 15 = 15(x + 10)/x - 0.25(x + 10)
Then we'll multiply both sides of the equation by x to get: 15x = 15(x + 10) - 0.25(x + 10)(x)
Expand: 15x = 15x + 150 - 0.25x² + 2.5x
Subtract 15x from both sides: 0 = 150 - 0.25x² - 2.5x
To make matters easier, let's multiply both sides of the equation by 4 to get: 0 = 600 - x² - 10x
Rearrange to get: x² + 10x - 600 = 0
Factor: (x - 20)(x + 30) = 0

So, x = 20 or x = -30
Since B's cannot be negative, the correct answer is 20
avatar
S
COolguy101
Senior Manager
Senior Manager
Joined: 23 Jan 2021
Posts: 294
Own Kudos [?]: 172 [0]
Given Kudos: 81
Concentration: , International Business
Send PM
Two people walk the same distance of 15miles, in which A spends 15 min [#permalink] New post   13 Aug 2021, 07:22
GreenlightTestPrep wrote:
The speed of B is 10 miles/h slower than the speed of A
Let x = B's speed (in miles per hour)
So, x + 10 = A's speed (in miles per hour)

A spends 15 minutes less than B
Time = distance/rate
So, B's travel time = 15/x
And A's travel time = 15/(x + 10)

Since we're dealing with rates measured in miles per HOUR, will convert 15 minutes to 0.25 HOURS
We can write: (A's travel time) = (B's travel time) - 0.25
Substitute to get: 15/(x + 10) = 15/x - 0.25

To solve for x, will first multiply both sides of the equation by (x + 10) to get: 15 = 15(x + 10)/x - 0.25(x + 10)
Then we'll multiply both sides of the equation by x to get: 15x = 15(x + 10) - 0.25(x + 10)(x)
Expand: 15x = 15x + 150 - 0.25x² + 2.5x
Subtract 15x from both sides: 0 = 150 - 0.25x² - 2.5x
To make matters easier, let's multiply both sides of the equation by 4 to get: 0 = 600 - x² - 10x
Rearrange to get: x² + 10x - 600 = 0
Factor: (x - 20)(x + 30) = 0

So, x = 20 or x = -30
Since B's cannot be negative, the correct answer is 20


:please: :please: :heart
Prep Club for GRE Bot
gmatclubot
Two people walk the same distance of 15miles, in which A spends 15 min [#permalink]
13 Aug 2021, 07:22
Moderators:
adewale223
GRE Instructor
88 posts
bronaugust
GRE Forum Moderator
37 posts
BrushMyQuant
Moderator
1115 posts
VibhuAnurag
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Main navigation

Partners

GRE Resources

www.ets.org/gre | About | Terms and Conditions and Privacy Policy | Prep Club for GRE Rules | Contact