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

 It is currently 21 Jan 2019, 12:32

### 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

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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### GMAT Club Tests are Free & Open for Martin Luther King Jr.'s Birthday!

January 21, 2019

January 21, 2019

10:00 PM PST

11:00 PM PST

Mark your calendars - All GMAT Club Tests are free and open January 21st for celebrate Martin Luther King Jr.'s Birthday.
• ### The winners of the GMAT game show

January 22, 2019

January 22, 2019

10:00 PM PST

11:00 PM PST

In case you didn’t notice, we recently held the 1st ever GMAT game show and it was awesome! See who won a full GMAT course, and register to the next one.

# A person can walk at a constant rate of 8mph and can bike at a rate of

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Aug 2009
Posts: 7212
A person can walk at a constant rate of 8mph and can bike at a rate of  [#permalink]

### Show Tags

Updated on: 19 May 2016, 08:50
1
15
00:00

Difficulty:

35% (medium)

Question Stats:

77% (02:16) correct 23% (02:15) wrong based on 354 sessions

### HideShow timer Statistics

A person can walk at a constant rate of 8mph and can bike at a rate of 16mph. If he wants to travel 80 miles in 8 hours using bike and walking at their constant rates, how much distance would he require to walk?

A. 20
B. 30
C. 48
D. 60
E. 72

OA after three days

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Originally posted by chetan2u on 26 Mar 2016, 03:31.
Last edited by Vyshak on 19 May 2016, 08:50, edited 1 time in total.
Math Expert
Joined: 02 Aug 2009
Posts: 7212
Re: A person can walk at a constant rate of 8mph and can bike at a rate of  [#permalink]

### Show Tags

26 Mar 2016, 04:36
3
3
Vyshak wrote:
Total distance = 80
Distance = Speed * Time
Walking speed = s1 = 8
Walking time = t1
Bike speed = s2 = 16
Time traveled in bike = t2

d1 + d2 = 80
s1t1 + s2t2 = 80
8*t1 + 16*t2 = 80
t1 + 2*t2 = 10 ----- (1)
Given: t1 + t2 = 8 ----- (2)

(1) - (2) --> t2 = 2 and t1 = 8 - 2 = 6

Walking distance = s1*t1 = 8*6 = 48

Hi Vyshak,
you are correct, BUT Alligation or Weighted average method..is the fastest method in such Qs
It enables us to find the ratio in which two or more ingredients at the given price/%/weight must be mixed to produce a mixture of a desired price/%/weight.

Lets manipulate this Q to fit into weighted average method--

here the walking speed= 8mph, so time he would take cover 80miles= 80/8=10 hr
similarly the biking speed= 16mph, so time he would take cover 80miles= 80/16=5 hr

But the average has to be 8hrs, so the ratio of dist by walking = $$\frac{(Avg-biking time)}{(walking time-biking time)}= \frac{(8-5)}{(10-5)}= \frac{3}{5}$$
so the distance travelled = 3/5 th of total = 3/5 *80 = 48
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

##### General Discussion
SC Moderator
Joined: 13 Apr 2015
Posts: 1687
Location: India
Concentration: Strategy, General Management
GMAT 1: 200 Q1 V1
GPA: 4
WE: Analyst (Retail)
Re: A person can walk at a constant rate of 8mph and can bike at a rate of  [#permalink]

### Show Tags

26 Mar 2016, 03:40
2
2
Total distance = 80
Distance = Speed * Time
Walking speed = s1 = 8
Walking time = t1
Bike speed = s2 = 16
Time traveled in bike = t2

d1 + d2 = 80
s1t1 + s2t2 = 80
8*t1 + 16*t2 = 80
t1 + 2*t2 = 10 ----- (1)
Given: t1 + t2 = 8 ----- (2)

(1) - (2) --> t2 = 2 and t1 = 8 - 2 = 6

Walking distance = s1*t1 = 8*6 = 48

Intern
Joined: 22 Dec 2015
Posts: 39
Re: A person can walk at a constant rate of 8mph and can bike at a rate of  [#permalink]

### Show Tags

19 May 2016, 08:42
Hi Chetan2u,

Current Student
Joined: 18 Oct 2014
Posts: 843
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
Re: A person can walk at a constant rate of 8mph and can bike at a rate of  [#permalink]

### Show Tags

19 May 2016, 09:13
3
I backsolved this question

Total distance= 80 miles
Total time= 8 hrs

First check for option 'C'

48 miles of walking means he walked for 48/8= 6 hrs
Remaining 32 miles of biking means he biked for 32/16= 2 hrs

Total hours traveled= 6+2 = 8hrs (as mentioned in the question stem)
_________________

I welcome critical analysis of my post!! That will help me reach 700+

Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4351
Location: India
GPA: 3.5
Re: A person can walk at a constant rate of 8mph and can bike at a rate of  [#permalink]

### Show Tags

20 May 2016, 11:28
1
chetan2u wrote:
A person can walk at a constant rate of 8 mph and can bike at a rate of 16mph. If he wants to travel 80 miles in 8 hours using bike and walking at their constant rates, how much distance would he require to walk?

A. 20
B. 30
C. 48
D. 60
E. 72

OA after three days

AN ALTERNATE APPROACH

Check the answer options , the correct answer for walking must be a multiple of 8 and for bike must be multiple of 16 , so possible answers are C. 48 & E. 72

Back solve

C. 48

Walk = 48 miles ; Bike = 32
Walking speed = 8 miles/hr ; Biking speed = 16 miles/hr
Walking time = 6 hr ; Biking speed = 2 hr ( total time is 8 hours )

E. 72

Walk = 72 miles ; Bike = 8
Walking speed = 8 miles/hr ; Biking speed = 16 miles/hr
Walking time = 9 hr ; Biking speed = 1/2 hr ( total time is 19/2 hours )

Hence correct answer must be (C)
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Intern
Joined: 14 Jun 2016
Posts: 17
Location: United States
GMAT 1: 700 Q48 V37
WE: Engineering (Pharmaceuticals and Biotech)
Re: A person can walk at a constant rate of 8mph and can bike at a rate of  [#permalink]

### Show Tags

20 Sep 2016, 16:34
chetan2u wrote:
A person can walk at a constant rate of 8mph and can bike at a rate of 16mph. If he wants to travel 80 miles in 8 hours using bike and walking at their constant rates, how much distance would he require to walk?

A. 20
B. 30
C. 48
D. 60
E. 72

OA after three days

time of bike: b
time of walk: w
b+w=8 -> b=8-w

D=Rt:
8w+16b =80
substitute b: 8w+16(8-w)=80. Solving for w and get w=6.
To get the total distance of walk, multiply 6 by 8 = 48. C
Manager
Joined: 29 Aug 2008
Posts: 110
Re: A person can walk at a constant rate of 8mph and can bike at a rate of  [#permalink]

### Show Tags

06 Oct 2016, 10:59
chetan2u wrote:
Vyshak wrote:
Total distance = 80
Distance = Speed * Time
Walking speed = s1 = 8
Walking time = t1
Bike speed = s2 = 16
Time traveled in bike = t2

d1 + d2 = 80
s1t1 + s2t2 = 80
8*t1 + 16*t2 = 80
t1 + 2*t2 = 10 ----- (1)
Given: t1 + t2 = 8 ----- (2)

(1) - (2) --> t2 = 2 and t1 = 8 - 2 = 6

Walking distance = s1*t1 = 8*6 = 48

Hi Vyshak,
you are correct, BUT Alligation or Weighted average method..is the fastest method in such Qs
It enables us to find the ratio in which two or more ingredients at the given price/%/weight must be mixed to produce a mixture of a desired price/%/weight.

Lets manipulate this Q to fit into weighted average method--

here the walking speed= 8mph, so time he would take cover 80miles= 80/8=10 hr
similarly the biking speed= 16mph, so time he would take cover 80miles= 80/16=5 hr

But the average has to be 8hrs, so the ratio of dist by walking = $$\frac{(Avg-biking time)}{(walking time-biking time)}= \frac{(8-5)}{(10-5)}= \frac{3}{5}$$
so the distance travelled = 3/5 th of total = 3/5 *80 = 48

chetan2u

Thanks for the solution, I was able to solve it using traditional method and was able to follow your weighted average method.

Can you pls explain that instead of using Average time taken for weighted average method, why can't we use directly the respective speeds given ( 8 mph, 16 mph etc).

TIA
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8803
Location: Pune, India
Re: A person can walk at a constant rate of 8mph and can bike at a rate of  [#permalink]

### Show Tags

06 Oct 2016, 20:56
1
3
chetan2u wrote:
A person can walk at a constant rate of 8mph and can bike at a rate of 16mph. If he wants to travel 80 miles in 8 hours using bike and walking at their constant rates, how much distance would he require to walk?

A. 20
B. 30
C. 48
D. 60
E. 72

OA after three days

gauravk

SpeedW - 8 mph
SpeedB - 16 mph

Avg speed = 80/8 = 10 mph

TW/TB = (SpeedB - SpeedAvg)/(SpeedAvg - SpeedW) = (16 - 10)/(10 - 8) = 3/1

So he walked for 3/4th of the time i.e. for (3/4)*8 hrs = 6 hrs. (Note that when averaging speed, the weights will always be time taken, never distance.)
In 6 hrs, he would have walked a distance of 8*6 = 48 miles

_________________

Karishma
Veritas Prep GMAT Instructor

Manager
Joined: 29 Aug 2008
Posts: 110
Re: A person can walk at a constant rate of 8mph and can bike at a rate of  [#permalink]

### Show Tags

06 Oct 2016, 22:50
VeritasPrepKarishma wrote:
chetan2u wrote:
A person can walk at a constant rate of 8mph and can bike at a rate of 16mph. If he wants to travel 80 miles in 8 hours using bike and walking at their constant rates, how much distance would he require to walk?

A. 20
B. 30
C. 48
D. 60
E. 72

OA after three days

gauravk

SpeedW - 8 mph
SpeedB - 16 mph

Avg speed = 80/8 = 10 mph

TW/TB = (SpeedB - SpeedAvg)/(SpeedAvg - SpeedW) = (16 - 10)/(10 - 8) = 3/1

So he walked for 3/4th of the time i.e. for (3/4)*8 hrs = 6 hrs. (Note that when averaging speed, the weights will always be time taken, never distance.)
In 6 hrs, he would have walked a distance of 8*6 = 48 miles

VeritasPrepKarishma

Thanks a lot for the explanation, I was going wrong with the highlighted part. I was using the ratio directly on the total distance (which obviously wasn't working).

Is there a mathematical derivation of the highlighted part which can help me understand this, rather than cramming it.

TIA.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8803
Location: Pune, India
Re: A person can walk at a constant rate of 8mph and can bike at a rate of  [#permalink]

### Show Tags

07 Oct 2016, 01:35
gauravk wrote:
VeritasPrepKarishma wrote:
chetan2u wrote:
A person can walk at a constant rate of 8mph and can bike at a rate of 16mph. If he wants to travel 80 miles in 8 hours using bike and walking at their constant rates, how much distance would he require to walk?

A. 20
B. 30
C. 48
D. 60
E. 72

OA after three days

gauravk

SpeedW - 8 mph
SpeedB - 16 mph

Avg speed = 80/8 = 10 mph

TW/TB = (SpeedB - SpeedAvg)/(SpeedAvg - SpeedW) = (16 - 10)/(10 - 8) = 3/1

So he walked for 3/4th of the time i.e. for (3/4)*8 hrs = 6 hrs. (Note that when averaging speed, the weights will always be time taken, never distance.)
In 6 hrs, he would have walked a distance of 8*6 = 48 miles

VeritasPrepKarishma

Thanks a lot for the explanation, I was going wrong with the highlighted part. I was using the ratio directly on the total distance (which obviously wasn't working).

Is there a mathematical derivation of the highlighted part which can help me understand this, rather than cramming it.

TIA.

Check here: https://www.veritasprep.com/blog/2014/1 ... -averages/
_________________

Karishma
Veritas Prep GMAT Instructor

VP
Joined: 05 Mar 2015
Posts: 1003
Re: A person can walk at a constant rate of 8mph and can bike at a rate of  [#permalink]

### Show Tags

26 Dec 2016, 11:30
chetan2u wrote:
A person can walk at a constant rate of 8mph and can bike at a rate of 16mph. If he wants to travel 80 miles in 8 hours using bike and walking at their constant rates, how much distance would he require to walk?

A. 20
B. 30
C. 48
D. 60
E. 72

OA after three days

similar approach by Vyshak and chetan2u but in different pattern

let distance covered by walking =W & by bike=B
As avg speed on travelling both by walking and bike=80km in 8 hrs==10km/hr

we can arrange in avg. speed formula=total distance /total time
(W+B)/{W/8+B/16}=10
(16W+16B)/(2W+B)=10
16W+16B=20W+10B
B=2/3W--------------(I)
as total distance W+B=80
putting value of B from (I)
W+2/3W=80
W=48

Ans C
Current Student
Status: Preparing for GMAT!!
Joined: 11 Oct 2015
Posts: 131
Location: India
GMAT 1: 660 Q47 V34
GMAT 2: 700 Q48 V38
GPA: 3.1
WE: General Management (Entertainment and Sports)
Re: A person can walk at a constant rate of 8mph and can bike at a rate of  [#permalink]

### Show Tags

27 Dec 2016, 09:15
1
chetan2u wrote:
A person can walk at a constant rate of 8mph and can bike at a rate of 16mph. If he wants to travel 80 miles in 8 hours using bike and walking at their constant rates, how much distance would he require to walk?

A. 20
B. 30
C. 48
D. 60
E. 72

OA after three days

W=Time spent walking
B=Time spent biking

80=16B+8W
=>W=10-2B
But, W+B=8 (given)
=>W=10-2(8-W)
=>W=6

=> Distance walked=6*8=48miles

C
_________________

Yours,
Siva Rama Krishna Meka

Non-Human User
Joined: 09 Sep 2013
Posts: 9463
Re: A person can walk at a constant rate of 8mph and can bike at a rate of  [#permalink]

### Show Tags

29 Dec 2017, 05:53
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: A person can walk at a constant rate of 8mph and can bike at a rate of &nbs [#permalink] 29 Dec 2017, 05:53
Display posts from previous: Sort by