speed

Expert replies

rupsk: Master | Next Rank: 500 Posts; Posts: 123; Joined: Mon Feb 07, 2011 12:11 pmFollowed by: 1 member

by rupsk » Thu Sep 01, 2011 3:04 pm

Traveling at three-fourth of his normal speed John reaches his office late by 16 minutes. Find the time taken by John to reach his office if he travels at his normal speed.</p>

A. 45 min
B. 48 minutes
C. 40 minutes
D. 50 minutes
E. 55 minutes

I had solved by looking at the answer is there any other way?

Like this post

Source: Beat The GMAT — Problem Solving | Thu Sep 01, 2011 3:04 pm

jarmitage23: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Sun Jun 26, 2011 6:17 pm

by jarmitage23 » Thu Sep 01, 2011 7:16 pm

I believe that if this question is treated as two scenarios, the first when he is on time and the second when he arrives 16 minutes later. By using the formula rt=d for boh scenarios. For the normal rate I assigned an arbitrary number - let's say 12 (a good number because it is a multiple of 4). If 12 is the normal speed then three quarters of 12, or 9, is the rate when he is late. Thenormal time it takes him to get to work is assigned variable t, therefore the delayed time is t+16. So scenario one (normal rate and time) would equal 12t and the slower rate and time would equal 9(t+16). Set these two equal to each other, 12t = 9(t+16) and solve. The normal time it takes him to get to work is 48 minutes, answer b.

I forget to mention why they are set equal to each other - when plugged into the rate formula they both equal distance.

12t = d and 9(t+16) = d

Also, this works for other arbitrary numbers not just 12, make sure you take three quarters of which ever number you select to obtain he slower rate.

Hope this explanation helps.

Jonathan

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Sep 01, 2011 7:30 pm

rupsk wrote:Traveling at three-fourth of his normal speed John reaches his office late by 16 minutes. Find the time taken by John to reach his office if he travels at his normal speed.</p>

A. 45 min
B. 48 minutes
C. 40 minutes
D. 50 minutes
E. 55 minutes

I had solved by looking at the answer is there any other way?

Traveling at 3/4 the speed = traveling for 4/3 the time.
Since the normal time is increased by 1/3:
16 = (1/3)t
t = 48.

The correct answer is B.

We also could plug in the answers:

Answer choice B: 48 minutes.
Let r = 4 miles per minute.
Then d = r*t = 4*48 = 192 miles.
3/4 the rate = (3/4)*4 = 3 miles per minute.
Time at the slower rate = d/r = 192/3 = 64 minutes.
Difference in time = 64-48 = 16. Success!

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

Like this post

saketk: Legendary Member; Posts: 608; Joined: Sun Jun 19, 2011 11:16 amFollowed by: 8 members; Thanked: 37 times

by saketk » Fri Sep 02, 2011 12:46 am

rupsk wrote:Traveling at three-fourth of his normal speed John reaches his office late by 16 minutes. Find the time taken by John to reach his office if he travels at his normal speed.</p>

A. 45 min
B. 48 minutes
C. 40 minutes
D. 50 minutes
E. 55 minutes

I had solved by looking at the answer is there any other way?

Hi-- I always wonder, how can test makers come up with so many different question on Time-Speed-Distance when there is only 1 simple formula Speed = Distance/Time? Irony!

That's the beauty of Math.
Well, lets concentrate on this question.

From the formula of TSD, we know that Speed is inversely proportional to Time

This means that if Time increases then Speed Decreases and Vice Versa.

It is given that travelling at (3/4)T John reaches 16 mins late.
Reverse this number and we have (4/3)T i.e 1/3rd extra of original time..
Equate this to the extra time John took..

(1/3)T= 16
or T=48 mins..

The correct answer is Option B

Like this post

xs4rahulgoel: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Mon May 12, 2008 8:16 am; Location: Noida

by xs4rahulgoel » Fri Sep 02, 2011 5:57 am

(d/t)(3/4) = d/(t+16)...solve for t. ans = 48

Like this post

Abhishek009: Master | Next Rank: 500 Posts; Posts: 359; Joined: Wed Mar 11, 2009 4:37 amFollowed by: 2 members; Location: Kolkata, India; Thanked: 50 times

by Abhishek009 » Fri Sep 02, 2011 6:27 am

rupsk wrote:Traveling at three-fourth of his normal speed John reaches his office late by 16 minutes. Find the time taken by John to reach his office if he travels at his normal speed.</p>

A. 45 min
B. 48 minutes
C. 40 minutes
D. 50 minutes
E. 55 minutes

I had solved by looking at the answer is there any other way?

There is a cool formula for solving such problem as follows :

If a person/body travels at a/b of his normal speed and the change in time taken to cover the same distance is t

Then the Change in time taken is

{( b/a) - 1 } * original time

Here a/b is 3/4 and change in time taken is 16

Now let's apply the formula

{ ( 4/3) - 1 } * original Time taken to cover the same distance = 16

Now ,

1/3 * Original Time = 16

Hence original time taken is 48....

Abhishek

Like this post

rupsk: Master | Next Rank: 500 Posts; Posts: 123; Joined: Mon Feb 07, 2011 12:11 pmFollowed by: 1 member

by rupsk » Fri Sep 02, 2011 6:29 am

thanks for all different solution, it gives me different direction to solve this kind of problem.

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review