GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 18 Nov 2018, 14:54

Close

GMAT 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 GMAT 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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • How to QUICKLY Solve GMAT Questions - GMAT Club Chat

     November 20, 2018

     November 20, 2018

     09:00 AM PST

     10:00 AM PST

    The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
  • The winning strategy for 700+ on the GMAT

     November 20, 2018

     November 20, 2018

     06:00 PM EST

     07:00 PM EST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

Bill and Ted each competed in a 240-mile bike race.

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3122
Location: Canada
Bill and Ted each competed in a 240-mile bike race.  [#permalink]

Show Tags

New post Updated on: 25 May 2017, 04:16
2
Top Contributor
7
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

74% (02:58) correct 26% (03:17) wrong based on 183 sessions

HideShow timer Statistics

Bill and Ted each competed in a 240-mile bike race. Bill’s average speed was 5 miles per hour slower than Ted’s average speed. If Ted completed the race 4 hours sooner than Bill did, what was Bill’s average speed in miles per hour?

A) 7.5
B) 10
C) 12
D) 12.5
E) 15

*Kudos for all correct solutions.

_________________

Test confidently with gmatprepnow.com
Image


Originally posted by GMATPrepNow on 26 Oct 2016, 11:43.
Last edited by GMATPrepNow on 25 May 2017, 04:16, edited 1 time in total.
Manager
Manager
avatar
Joined: 05 Jun 2015
Posts: 83
Location: United States
WE: Engineering (Transportation)
Re: Bill and Ted each competed in a 240-mile bike race.  [#permalink]

Show Tags

New post 26 Oct 2016, 17:04
1
1
Vb and Vt be the average speeds of Bill and Ted.
Vb = Vt - 5

Tb and Tt be the time take,
Tt = Tb - 4


We have Distance = Speed * Time
\(Vb* Tb = Vt * Tt = 240\)
\((Vt - 5) * ( Tt + 4) = Vt * Tt\)
4Vt - 5 Tt = 20
Replacing value of Tt as 240/Vt

\(4 Vt - 5*(\frac{240}{Vt}) = 20\)
\(Vt^{2} - 5 Vt = 300\)
\((Vt -20)* (Vt +15) = 0\)
Vt = 20

Average speed of Bill Vb = Vt-5 = 20- 5 = 15.
Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4170
Location: United States (CA)
Re: Bill and Ted each competed in a 240-mile bike race.  [#permalink]

Show Tags

New post 27 Oct 2016, 16:26
3
GMATPrepNow wrote:
Bill and Ted each competed in a 240-mile bike race. Bill’s average speed was 5 miles per hour slower than Ted’s average speed. If Ted completed the race 4 hours sooner than Bill did, what was Bill’s average speed in miles per hour?

A) 7.5
B) 10
C) 12
D) 12.5
E) 15


We are given that Bill and Ted each competed in a 240-mile bike race. We are also given that Bill’s average speed was 5 miles per hour slower than Ted’s average speed.

Both Bill and Ted had distance of 240 miles. If we let Ted’s speed = r, we can let Bill’s speed = r - 5. We can use the above information to determine the time of Bill and Ted in terms of variable r.

Since time = distance/rate, Ted’s time = 240/r and Bill’s time = 240/(r - 5).

Since Ted completed the race 4 hours sooner than Bill did, we can create the following equation:

240/r + 4 = 240/(r - 5)

To eliminate the denominators of the fractions we can multiply the entire equation by r(r-5) and we have:

240(r - 5) + 4[r(r - 5)] = 240r

240r - 1,200 + 4r^2 - 20r = 240r

4r^2 - 20r - 1,200 = 0

r^2 - 5r - 300 = 0

(r - 20)(r + 15) = 0

r = 20 or r = -15

Since r must be positive, r = 20.

Thus, Bill’s rate = 20 - 5 = 15 mph.

Answer: E
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Senior Manager
Senior Manager
User avatar
G
Joined: 03 Apr 2013
Posts: 278
Location: India
Concentration: Marketing, Finance
GMAT 1: 740 Q50 V41
GPA: 3
GMAT ToolKit User
Re: Bill and Ted each competed in a 240-mile bike race.  [#permalink]

Show Tags

New post 24 May 2017, 22:35
4
GMATPrepNow wrote:
Bill and Ted each competed in a 240-mile bike race. Bill’s average speed was 5 miles per hour slower than Ted’s average speed. If Ted completed the race 4 hours sooner than Bill did, what was Bill’s average speed in miles per hour?

A) 7.5
B) 10
C) 12
D) 12.5
E) 15

*Kudos for all correct solutions.

You can find our video solution here: https://www.gmatprepnow.com/module/gmat ... /video/947


Another way to build up the quadratic...

Let Bill's speed = x
and Ted's speech = x+5

When Ted covers the full distance, Bill has yet to travel for 4 more hours to complete the distance
\(\frac{240}{(240 - 4x)} = \frac{(x + 5)}{x}\)
_________________

Spread some love..Like = +1 Kudos :)

CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3122
Location: Canada
Re: Bill and Ted each competed in a 240-mile bike race.  [#permalink]

Show Tags

New post 25 May 2017, 04:14
1
Top Contributor
GMATPrepNow wrote:
Bill and Ted each competed in a 240-mile bike race. Bill’s average speed was 5 miles per hour slower than Ted’s average speed. If Ted completed the race 4 hours sooner than Bill did, what was Bill’s average speed in miles per hour?

A) 7.5
B) 10
C) 12
D) 12.5
E) 15

*Kudos for all correct solutions.



Another approach....

Bill’s average speed was 5 miles per hour slower than Ted’s average speed.
Let B = Bill's travel speed
So, B + 5 = Ted's average speed

Ted completed the race 4 hours sooner than Bill did
Let's start with a word equation:
(Bill's travel time) = (Ted's travel time) + 4
time = distance/speed
So, we get: 240/B = 240/(B + 5) + 4
Rewrite 4 as 4(B + 5)/(B + 5) to get: 240/B = 240/(B + 5) + 4(B + 5)/(B + 5)
Simplify: 240/B = 240/(B + 5) + (4B + 20)/(B + 5)
Combine terms: 240/B = (4B + 260)/(B + 5)
Cross multiply: 240(B + 5) = (B)(4B + 260)
Expand and simplify: 240B + 1200 = 4B² + 260B
Set equal to zero: 4B² + 20B - 1200 = 0
Divide both sides by 4 to get: B² + 5B - 300 = 0
Factor: (B + 20)(B - 15) = 0
So, EITHER B = -20 OR B = 15
Since B (Bill's speed) cannot be a negative value, we can conclude that B = 15.

Answer:

RELATED VIDEO

_________________

Test confidently with gmatprepnow.com
Image

Director
Director
User avatar
P
Joined: 13 Mar 2017
Posts: 630
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: Bill and Ted each competed in a 240-mile bike race.  [#permalink]

Show Tags

New post 23 Oct 2017, 22:22
1
GMATPrepNow wrote:
Bill and Ted each competed in a 240-mile bike race. Bill’s average speed was 5 miles per hour slower than Ted’s average speed. If Ted completed the race 4 hours sooner than Bill did, what was Bill’s average speed in miles per hour?

A) 7.5
B) 10
C) 12
D) 12.5
E) 15

*Kudos for all correct solutions.


Let Ted's average speed be x miles/hr.
Bill's average speed be x-5 miles/hr.

Distance = 240 miles

240/(x-5) - 240/x = 4
240*5/(x(x-5)) = 4
x(x-5) = 300
x = 20
x-5 = 15

Answer E
_________________

CAT 2017 99th percentiler : VA 97.27 | DI-LR 96.84 | QA 98.04 | OA 98.95
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu


Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)



What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".

Manager
Manager
avatar
B
Joined: 03 May 2014
Posts: 161
Location: India
WE: Sales (Mutual Funds and Brokerage)
Bill and Ted each competed in a 240-mile bike race.  [#permalink]

Show Tags

New post 03 Nov 2017, 03:44
1
Easier method
Bills time be= t and speed=x
Ted's time=t-4 and speed=x+5
distance =240
Bill's time(t) = distance/speed=240/x
Teds time(t-4)=240/(x+5)

Plugin answer choices. you should start from c or answers which are whole numbers

Let bills speed be =15
we now have
Bill(t)=240/15=16
Now Plugin for ted
t-4=240/(15+5)=240/20=12 or t=12+4=16.
with above approach we can avoid quadratic equation.
VP
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1114
Bill and Ted each competed in a 240-mile bike race.  [#permalink]

Show Tags

New post 04 Nov 2017, 14:19
1
GMATPrepNow wrote:
Bill and Ted each competed in a 240-mile bike race. Bill’s average speed was 5 miles per hour slower than Ted’s average speed. If Ted completed the race 4 hours sooner than Bill did, what was Bill’s average speed in miles per hour?

A) 7.5
B) 10
C) 12
D) 12.5
E) 15

*Kudos for all correct solutions.


let r=Bill's average speed
Bill: d=rt
Ted: d=(r+5)(t-4)
combining,
rt=(r+5)(t-4)➡
4r=5t-20
substituting,
4r=5(240/r)-20➡
r^2+5r-300=0
(r+20)(r-15)=0
r=15 mph
E
GMAT Club Bot
Bill and Ted each competed in a 240-mile bike race. &nbs [#permalink] 04 Nov 2017, 14:19
Display posts from previous: Sort by

Bill and Ted each competed in a 240-mile bike race.

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.