A hiker walks three sections of a trail that are of equal length. The

Question

A hiker walks three sections of a trail that are of equal length. The first section of the trail is flat, and on this section the hiker travels at 3 miles per hour for 1.5 hours. The second section is uphill, and on this section the hiker’s pace slows by 25 percent. The third section is downhill, and here his speed doubles. What was the hiker’s average speed for the entire three-section hike?

A. 1.5
B. 3
C. 3.25
D. 4.5
E. 9.75

A. 1.5
B. 3
C. 3.25
D. 4.5
E. 9.75

GMATWhizTeam · Answer

Solution:  
 • All the three sections are of equal length.
• Speed in first section = 3 miles per hour
 o Distance of first section = 3*1.5 = 4.5 miles 
• Speed in second section =  3-\frac{25}{100}*3  = 9/4 miles/hr
 o Time taken to cover second section =  4.5*\frac{4}{9} = 2  hr 
• Speed in third section =  2*\frac{9}{4} = \frac{18}{4} 
 o Time taken to cover third section =  4.5*\frac{4}{18}=1  hr 
• Average speed =  \frac{(Total distance)}{(Total time)}  = \frac{(4.5+4.5+4.5)}{(1.5+2+1)} = \frac{13.5}{4.5}  =  3 \frac{miles}{hr}  
Hence, the correct answer is  Option B .

Fdambro294 · Answer

All 3 sections have the same distance which we can find from section 1:

(3 mph) * (1.5 hours) = 4.5 miles

Total Distance = (3) (4.5) miles

Section 2: the speed decreases by (1/4) ——-since distance is constant, meaning speed is inversely proportional to time traveled———this means Time will INCREASE by (1/3)

(1.5 hr) + (1/3)(1.5) =

(4/3) (1.5) = 2 hours

Finally, distance is constant again for the 3rd section.

Speed increases by a Factor of * (2) ——-> 2 times

Time traveled must therefore DECREASE by a Factor of * (1/2) ————-> (1/2) Times prior time traveled.

(1/2) * (2 hours) = 1 hour

Total Time = (1.5) + (2) + (1) = 4.5 hours

Avg speed = Total D / Total T =

(3) (4.5) / 4.5 =

3 kmph

Posted from my mobile device

rahulms94 · Answer

I'm a bit confused.
The question says the speed has doubled in the third section.

So, shouldn't this mean that the speed = 3*2 = 6mph??
Why did we double the speed of his uphill task??? It wasn't clearly mentioned was it?

Would appreciate an explanation.

Thanks!

andreagonzalez2k · Answer

I think the same. It isn't clear enough.

apurv09 · Answer

if its not mentioned that his speed in the first section doubled, then we will have to consider the present speed . which is the speed in 2nd second. because "his speed" means speed at which he is currently travelling in.

GMATGuruNY · Answer

I believe that the blue portion below reflects the intent of the problem-writer:

Total distance of the 3-section trail = 3 * (rate for the first section * time for the first section) = 3 * (3*1.5) = 13.5 miles

Rate and time have a RECIPROCAL RELATIONSHIP.

Since the rate for the second section is 3/4 the rate for the first section, the time for the second section is 4/3 the time for the first section:
4/3 * 3/2 = 2 hours

Since the rate for the third section is 2 times the rate for the second section, the time for the third section is 1/2 the time for the second section:
1/2 * 2 = 1 hour

Average speed  = \frac{total-distance}{total-time} = \frac{13.5}{1.5+2+1} = \frac{13.5}{4.5} = 3  miles per hour

B

Kinshook · Answer

Given: A hiker walks three sections of a trail that are of equal length. The first section of the trail is flat, and on this section the hiker travels at 3 miles per hour for 1.5 hours. The second section is uphill, and on this section the hiker’s pace slows by 25 percent. The third section is downhill, and here his speed doubles.

Asked: What was the hiker’s average speed for the entire three-section hike?

Total distance = 3*3*1.5 = 13.5 miles
Total time = 1.5 + 1.5/.75 + 1.5/2*.75 = 1.5 + 2 + 1 = 4.5 hours
Average speed = 13.5 /4.5 miles/hour = 3 miles/hour

IMO B

Rishm · Answer

GMAT test these, his speed doubled the previous speed and not the original speed. Hence, we see this.

A hiker walks three sections of a trail that are of equal length. The

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