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by oquiella » Mon Oct 05, 2015 4:43 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
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by [email protected] » Mon Oct 05, 2015 4:57 pm
HI oquiella,

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: B

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by GMATGuruNY » Mon Oct 05, 2015 6:06 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
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.
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