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

Redeem

average speed

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 72
Joined: Tue Nov 05, 2013 4:35 pm
Followed by:4 members

average speed

by Ankitaverma » Wed Nov 20, 2013 12:18 pm
A hiker walked for two days. On the second day the hiker walked 2 hours longer and at an average speed 1 mile per hour faster than he walked on the first day. If during the two days he walked a total of 64 miles and spent a total of 18 hours walking, what was his average speed on the first day?
(A) 2 mph
(B) 3 mph
(C) 4 mph
(D) 5 mph
(E) 6 mph[/b]
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 768
Joined: Wed Dec 28, 2011 4:18 pm
Location: Berkeley, CA
Thanked: 387 times
Followed by:140 members

by Mike@Magoosh » Wed Nov 20, 2013 1:06 pm
Ankitaverma wrote:A hiker walked for two days. On the second day the hiker walked 2 hours longer and at an average speed 1 mile per hour faster than he walked on the first day. If during the two days he walked a total of 64 miles and spent a total of 18 hours walking, what was his average speed on the first day?
(A) 2 mph
(B) 3 mph
(C) 4 mph
(D) 5 mph
(E) 6 mph[/b]
Dear Ankitaverma
I'm happy to help. :-) Here's a blog on distance, rate, and time:
https://magoosh.com/gmat/2012/gmat-math-rate-questions/

For this question --- Day #2, hiker walks for 2 hours more than the first day, for a total of 18 hours of walking. That means 8 hr of walking the first day, and 10 hours of walking the second day. I think backsolving is much easier and more efficient than an algebraic approach
https://magoosh.com/gmat/2012/gmat-plugg ... -choice-c/
Starting with (C)
If he walks 4 mph for 8 hours on Day 1 = 32 mi
Then 5 mph for 10 hours on Day 2 = 50 mi
Total = 32 + 50 = 82
Too much distance. Choices (C) & (D) & (E) are incorrect.

Try (B).
Day 1: 3 mph for 8 hours = 24 mi
Day 2: 4 mph for 10 hours = 40 mi
Total = 64 mi.
That's it! Answer = (B).

Does all this make sense?
Mike :-)
Magoosh GMAT Instructor
https://gmat.magoosh.com/
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Thu Nov 21, 2013 12:01 am
Hi Ankitaverma,

These types of questions are usually easier to handle if you create a table to organize your information, although you're going to have to do some algebra no matter how you organize.

We're told about 2 days (Day 2 was 2 hours longer and at a speed that was 1 mph more than Day 1). The information implies that we'll use the Distance Formula:

Distance = Rate x Time

Day 1: D = R x T
Day 2: D = (R+1) x (T+2)

Then we're told that the TOTAL Distance = 64 miles and the TOTAL Time was 18 hours.

Since the 2 "times" add up to 18 hours, we know:

T + (T+2) = 18
2T = 16
T = 8
This gives us:

Day 1: D = R x 8
Day 2: D = (R+1) x 10

We know the total distance is sum of the two "distances":

64 miles = 8R + 10(R+1)
64 = 8R + 10R + 10
54 = 18R
3 = R

The question asks us for the rate on Day 1 (so, what is R?)

Final Answer: [spoiler]B: 3[/spoiler]

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Thu Nov 21, 2013 4:17 am
Ankitaverma wrote:A hiker walked for two days. On the second day the hiker walked 2 hours longer and at an average speed 1 mile per hour faster than he walked on the first day. If during the two days he walked a total of 64 miles and spent a total of 18 hours walking, what was his average speed on the first day?
(A) 2 mph
(B) 3 mph
(C) 4 mph
(D) 5 mph
(E) 6 mph[/b]
The answer choices represent the slower speed.
The average speed for the entire trip = 64/18 ≈ 3.5 miles per hour.
Thus, the slower speed must be LESS than 3.5 miles per hour, while the faster speed must be GREATER than 3.5 miles per hour.
The difference between the two speeds is 1 mile per hour.
Only answer choice B -- which implies a slower speed of 3 miles per hour and a faster speed of 4 miles per hour -- is viable.

The correct answer is B.
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
Master | Next Rank: 500 Posts
Posts: 447
Joined: Fri Nov 08, 2013 7:25 am
Thanked: 25 times
Followed by:1 members

by Mathsbuddy » Thu Nov 21, 2013 6:40 am
If v = average speed on day 1
and t = total time on day 1
and using distance = V * T:

Total distance = 64 = [d1] + [d2]
64 = [vt] + [(v+1)(t+2)] EQUATION A

Also,total time = 18 = [t] + [t+2] = 2t + 2
So t =8

Substitute t=8 into equation A:
64 = 8v + (v+1)(8+2)
54 = 18v
v = 3
Top
Post new topic Post Reply
• Page 1 of 1