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
_________________

Verbal:new-to-the-verbal-forum-please-read-this-first-77546.html
Math: new-to-the-math-forum-please-read-this-first-77764.html
Gmat: everything-you-need-to-prepare-for-the-gmat-revised-77983.html
-------------------------------------------------------------------------------------------------
Ajit

ron covered this problem in his workshop on Rate/Time/Distance (April 29, 2010)
http://www.manhattangmat.com/thursdays-with-ron.cfm

yep, liked the 10 sec app as well...
_________________

GMAT Club Premium Membership - big benefits and savings

Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE


_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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?

Hiker walked for two days for a total of 18 hours. He spent two more hours walking on the second day than the first: h1+h2=18 ===> h+h+2 = 18 ===> 2h = 16 ===> h=8.
He spent 8 hours the first day and 10 hours the second day.
Day 1 = 8h
Day 2 = 10h

Average speed = total distance/combined rate
Average speed = 64/r1+r2

rate = distance/time
r = d/8
r+1 = d/10 ===> r = (d/10)-1

64/(d/8) + (d/10)-1

Why wouldn't I use that formula? Is it because I would be trying to figure out average speed when I don't know the speed of the hiker on day one or two?

distance=rate*time
d1=r*8
d2=(r+1)*10

d1+d2=total distance
d1+d2=64
(r8)+(10r+10)=64
18r=64
r=3

ANSWER: (B) 3 mph

Hi All,

This question requires a certain degree of note-taking and organization. Once you've got everything on the pad, you can then approach the math in a couple of ways:

Since we're dealing with distance, rate and time, I'm going to make two equations based on the two days of travel:

Day 1: Distance = (R mph)(T hours)
Day 2: Distance#2 = (R+1 mph)(T+2 hours)

Since the TOTAL TIME for both days was 18 hours, we can solve for T...

T + (T+2) = 18
2T = 16
T = 8

Since the TOTAL DISTANCE for both days was 64 miles, we can now set up 1 gigantic equation....

64 miles = (R)(8) + (R+1)(10)

At this point, we have 1 variable and 1 equation, so we can solve for R....

64 = 8R + 10R + 10
54 = 18R
3 = R

The prompt asks for the speed on DAY 1; since the hiker traveled R mph on Day 1, the answer is 3...

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************