BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

A marathoner ran for two days.

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 10
Joined: Tue Oct 15, 2013 4:45 am
by aaron1981 » Wed Jul 19, 2017 12:49 am
A marathoner ran for two days. On the second day, he ran at an average speed of 3 miles per hour faster than he ran on the first day. If during the two days he ran a total of 36 miles and did a total of 8 hours running, which of the following could be his average speed, in miles per hour, on the first day?

(A) 0.25
(B) 0.50
(C) 1.00
(D) 1.50
(E) 2.00

OA E
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members
Location: Grand Central / New York
Thanked: 470 times

by Jay@ManhattanReview » Wed Jul 19, 2017 1:19 am
aaron1981 wrote:A marathoner ran for two days. On the second day, he ran at an average speed of 3 miles per hour faster than he ran on the first day. If during the two days he ran a total of 36 miles and did a total of 8 hours running, which of the following could be his average speed, in miles per hour, on the first day?

(A) 0.25
(B) 0.50
(C) 1.00
(D) 1.50
(E) 2.00

OA E
Let the marathoner's speed on the first day be x miles per hour.

Thus, his speed on the second day was „(x ‚+ 3)… miles per hour.

Let the time for which the marathoner ran on the first day be t hours.

Thus, the time for which he ran on the second day ƒ „(8 - t)… hours.

Distance covered by him on the first day = „x *t… miles.

Distance covered by him on the second day = („„x ‚+ 3)*…(8 - t)…… miles.

Thus, total distance covered in two days = [†xt ‚+ („„x ‚+ 3)*…(8 - t)]…‡ miles.

Thus, we have:

xt ‚+ („„x ‚+ 3)*…(8 - t) = ƒ 36
=ƒ> xt ‚+ 8x - xt ‚ + 24 - 3t ƒ= 36
ƒ=> 8x ƒ= 3t ‚+ 12

Since this is a single linear equation with two variables, we cannot get the unique value of x;
however, we can get consistent values of x.

Working with the options one at a time:

Option A: x = 0.25 ƒ=> t ƒ= -10/3 -- Not possible, since t cannot be negative.

We see that since this is a 'Could be the value' type of question and that the smallest
option value of x yields a negative value for t, thus we should first try the largest value of x.

Option E: x ƒ= 2 ƒ=> t ƒ= 4/3 - Possible

Thus, we have x ƒ= 2. We need not check other options as the only option must be correct.

The correct answer: E

Hope this helps!

Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Bangkok | Abu Dhabi | Rome | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
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 » Wed Jul 19, 2017 1:25 am
aaron1981 wrote:A marathoner ran for two days. On the second day, he ran at an average speed of 3 miles per hour faster than he ran on the first day. If during the two days he ran a total of 36 miles and did a total of 8 hours running, which of the following could be his average speed, in miles per hour, on the first day?

(A) 0.25
(B) 0.50
(C) 1.00
(D) 1.50
(E) 2.00
The average speed for the entire two days must be BETWEEN the slower speed on the first day and the faster speed on the second day.
Average speed for the entire two days = (total distance over the two days)/(total time over the two days) = (36 miles)/(8 hours) = 9/2 = 4.5 miles per hour.

We can PLUG IN THE ANSWERS, which represent the speed on the first day.
Since the speed on the second day is 3mph faster than the speed on the first day, we get the following options:
A: 0.25 mph on the first day, 3.25 mph on the second day
B: 0.5 mph on the second day, 3.5 mph on the second day
C: 1 mph on the first day, 4 mph on the second day
D: 1.5 mph on the first day, 4.5 mph on the second day
E: 2 mph on the first day, 5 mph on the second day

Since the average speed for the entire two days -- 4.5 mph -- must between the slower speed and the faster speed, only the option in blue is viable.

The correct answer is E.
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
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members
Location: Grand Central / New York
Thanked: 470 times

by Jay@ManhattanReview » Wed Jul 19, 2017 1:27 am
aaron1981 wrote:A marathoner ran for two days. On the second day, he ran at an average speed of 3 miles per hour faster than he ran on the first day. If during the two days he ran a total of 36 miles and did a total of 8 hours running, which of the following could be his average speed, in miles per hour, on the first day?

(A) 0.25
(B) 0.50
(C) 1.00
(D) 1.50
(E) 2.00

OA E
Let us see this question from another approach.

Average speed of the marathoner for the two days ƒ= (Total distance) / (Total time) = 36/8 = 4.5 miles per hour

Say the average speed on the first day be x miles per hour, thus, the average speed on the second day
would be „(x +‚ 3)… miles per hour

Thus, the average speed of 4.5 miles per hour must lie between the values of the speeds on the two days.

Thus, we have:

x < 4.5 < x ‚+ 3

Among the options, only x ƒ= 2 satisfies.

The correct answer: E

Hope this helps!

Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Bangkok | Abu Dhabi | Rome | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8139
Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members
Location: Los Angeles, CA
Thanked: 43 times

Re: A marathoner ran for two days.

by Scott@TargetTestPrep » Fri Feb 21, 2020 7:33 am
aaron1981 wrote: ↑
Wed Jul 19, 2017 12:49 am
 A marathoner ran for two days. On the second day, he ran at an average speed of 3 miles per hour faster than he ran on the first day. If during the two days he ran a total of 36 miles and did a total of 8 hours running, which of the following could be his average speed, in miles per hour, on the first day?

(A) 0.25
(B) 0.50
(C) 1.00
(D) 1.50
(E) 2.00

OA E
The average speed for the entire two days was 36/8 = 4.5 mph

Thus, since the speed on the first day was 3 mph slower than that of the second day, the speed on the first day must be less than 4.5 mph and the speed on the second day must be greater than 4.5 mph.

Since the speed on the second day is greater than 4.5 mph, which is 3 mph faster than that of the first day, the speed on the first day must be greater than 1.5 mph. So the only possible speed on the first day, from the given answer choices, is 2 mph.

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1