Distance "Word" Problems

Expert replies

Smriti Shashikumar: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Sat Feb 16, 2013 9:29 am

by Smriti Shashikumar » Mon Feb 18, 2013 4:32 am

Cathy and Tom are 20 miles apart and walk towards each other along the same route. Cathy walks at a constant rate that is 1 mile per hour faster than that of Tom's constant rate of 5 miles per hour. If Tom starts his journey 24 minutes after Cathy, how far from his original destination has Tom walked when the two meet?

A. 7 miles
B. 8 miles
C. 9 miles
D. 10 miles
E. 12 miles

Thanks for the help as always!

Like this post

Source: Beat The GMAT — Problem Solving | Mon Feb 18, 2013 4:32 am

guerrero: Master | Next Rank: 500 Posts; Posts: 227; Joined: Sun Apr 08, 2012 4:53 amFollowed by: 3 members; Thanked: 12 times

by guerrero » Mon Feb 18, 2013 5:35 am

Smriti Shashikumar wrote:Cathy and Tom are 20 miles apart and walk towards each other along the same route. Cathy walks at a constant rate that is 1 mile per hour faster than that of Tom's constant rate of 5 miles per hour. If Tom starts his journey 24 minutes after Cathy, how far from his original destination has Tom walked when the two meet?

A. 7 miles
B. 8 miles
C. 9 miles
D. 10 miles
E. 12 miles

Thanks for the help as always!

your equation would be -

5*(t-24/20)+6*t=20
t=2hrs

t= this is the time when they meet

Therefore,Tom would have traveled - 8 miles . (B) Ans

Last edited by guerrero on Mon Feb 18, 2013 6:26 am, edited 1 time in total.

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 » Mon Feb 18, 2013 6:10 am

Smriti Shashikumar wrote:Cathy and Tom are 20 miles apart and walk towards each other along the same route. Cathy walks at a constant rate that is 1 mile per hour faster than that of Tom's constant rate of 5 miles per hour. If Tom starts his journey 24 minutes after Cathy, how far from his original destination has Tom walked when the two meet?

A. 7 miles
B. 8 miles
C. 9 miles
D. 10 miles
E. 12 miles

Thanks for the help as always!

Before Tom starts to walk, Cathy travels alone at rate of 6 miles per hour for 2/5 of an hour:
Distance = r*t = 6*(2/5) = 12/5 miles.
Remaining distance = 20 - 12/5 = 88/5 miles.
When people travel toward each other, they WORK TOGETHER to cover the distance between them, so we ADD THEIR RATES.
Combined rate for Cathy and Tom = 6+5 = 11 miles per hour.
Since Tom's rate is 5 miles per hour, Tom will travel 5 of every 11 miles traveled by Cathy and Tom together.
Thus, Tom will travel 5/11 of the remaining distance:
(5/11)(88/5) = 8 miles.

The correct answer is B.

Last edited by GMATGuruNY on Mon Feb 18, 2013 9:48 am, edited 1 time in total.

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

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Feb 18, 2013 8:24 am

Smriti Shashikumar wrote:Cathy and Tom are 20 miles apart and walk towards each other along the same route. Cathy walks at a constant rate that is 1 mile per hour faster than that of Tom's constant rate of 5 miles per hour. If Tom starts his journey 24 minutes after Cathy, how far from his original destination has Tom walked when the two meet?

A. 7 miles
B. 8 miles
C. 9 miles
D. 10 miles
E. 12 miles

I like to begin most speed/distance/time questions with a word equation.
One possible word equation is:
Cathy's travel time = Tom's travel time + 24 minutes

Another word equation is:
Cathy's distance + Tom's distance = 20 miles

Either of these word equations will yield the correct response. Let's continue with the second one.
Let t = Tom's travel time
So, t + 24 minutes = Cathy's travel time
Since our speeds are in miles per hour, we can also say...
So, t + 24/60 hours = Cathy's travel time

Cathy's distance = (speed)(time)
= (6)(t + 24/60)
= 6t + 12/5

Tom's distance = (speed)(time)
= (5)(t)
= 5t

So, we get: Cathy's distance + Tom's distance = 20 miles
6t + 12/5 + 5t = 20
Simplify: 11t + 12/5 = 20
Multiply both sides by 5: 55t + 12 = 100
Simplify: 55t = 88
Divide both sides by 11: 5t = 8

IMPORTANT: Since we already determined that Tom's distance = 5t, we can now see that this equals 8

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Feb 18, 2013 8:35 am

Smriti Shashikumar wrote:Cathy and Tom are 20 miles apart and walk towards each other along the same route. Cathy walks at a constant rate that is 1 mile per hour faster than that of Tom's constant rate of 5 miles per hour. If Tom starts his journey 24 minutes after Cathy, how far from his original destination has Tom walked when the two meet?

A. 7 miles
B. 8 miles
C. 9 miles
D. 10 miles
E. 12 miles

In my previous post, I used one of two word equations to answer the question. Let's examine another possible word equation.

Since Cathy traveled 24 minutes longer than Tom did, we can write:
Cathy's travel time = Tom's travel time + 24 minutes

Since 24 minutes = 2/5 hours, we can also write:
Cathy's travel time = Tom's travel time + 2/5 hours

We're trying to find the distance Tom traveled, so:
Let D = Tom's distance traveled.
Since their combined distances is 20 miles, we can say:
20-D = Cathy's distance traveled.

Cathy's travel time = distance/speed
= (20-D)/6

Tom's travel time = distance/speed
= D/5

So...
Cathy's travel time = Tom's travel time + 2/5 hours
(20-D)/6 = D/5 + 2/5
Simplify: (20-D)/6 = (D+2)/5
Cross multiply: 5(20-D) = 6(D+2)
Expand: 100 - 5D = 6D + 12
Rearrange: 88 = 11D
Solve: 8 = D

Since D = Tom's travel distance, the correct answer is B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 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