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23 Mar 2020, 05:23
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
55% (02:40) correct
45%
(03:25)
wrong
based on 422
sessions
History
Date
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Not Attempted Yet
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
23 Mar 2020, 08:18
Kudos
Bookmarks
Bunuel
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
- o Time taken to cover second section = \(4.5*\frac{4}{9} = 2\) hr
- o Time taken to cover third section = \(4.5*\frac{4}{18}=1\) hr
26 Mar 2021, 23:00
Kudos
Bookmarks
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
(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
