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John and Steve are speedwalkers in a race. John is 15 meters behind

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John and Steve are speedwalkers in a race. John is 15 meters behind [#permalink]

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New post 21 Aug 2015, 04:46
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John and Steve are speed walkers in a race. John is 15 meters behind Steve when he begins his final push. John blazes to the finish at a pace of 4.2 m/s, while Steve maintains a blistering 3.7 m/s speed. If John finishes the race 2 meters ahead of Steve, how long was John’s final push?

A. 13 seconds
B. 17 seconds
C. 26 seconds
D. 34 seconds
E. 51 seconds

Kudos for a correct solution.

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Joined: 20 Mar 2014
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Re: John and Steve are speedwalkers in a race. John is 15 meters behind [#permalink]

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New post 21 Aug 2015, 05:07
2
Bunuel wrote:
John and Steve are speed walkers in a race. John is 15 meters behind Steve when he begins his final push. John blazes to the finish at a pace of 4.2 m/s, while Steve maintains a blistering 3.7 m/s speed. If John finishes the race 2 meters ahead of Steve, how long was John’s final push?

A. 13 seconds
B. 17 seconds
C. 26 seconds
D. 34 seconds
E. 51 seconds

Kudos for a correct solution.


Let t be the time that John spent for his final push.

Thus, per the question,

4.2t = 3.7t+15+2 ---> 0.5t = 17 ---> t = 34 seconds.

D is the correct answer.
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Re: John and Steve are speedwalkers in a race. John is 15 meters behind [#permalink]

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New post 21 Aug 2015, 05:23
1
Bunuel wrote:
John and Steve are speed walkers in a race. John is 15 meters behind Steve when he begins his final push. John blazes to the finish at a pace of 4.2 m/s, while Steve maintains a blistering 3.7 m/s speed. If John finishes the race 2 meters ahead of Steve, how long was John’s final push?

A. 13 seconds
B. 17 seconds
C. 26 seconds
D. 34 seconds
E. 51 seconds

Kudos for a correct solution.


let Steve's distance during his final push be 'd'
d/3.7 =(d+17)/4.2
solving we get d=125.3m
time taken by steve is 125.3/3.7 = 34 seconds.
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Re: John and Steve are speedwalkers in a race. John is 15 meters behind [#permalink]

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New post 21 Aug 2015, 06:10
1
Bunuel wrote:
John and Steve are speed walkers in a race. John is 15 meters behind Steve when he begins his final push. John blazes to the finish at a pace of 4.2 m/s, while Steve maintains a blistering 3.7 m/s speed. If John finishes the race 2 meters ahead of Steve, how long was John’s final push?

A. 13 seconds
B. 17 seconds
C. 26 seconds
D. 34 seconds
E. 51 seconds

Kudos for a correct solution.


J is behind S by 15 m
Relative speed=4.2-3.7=0.5m/s(meaning in 1 s, J covers 0.5 m more than S)
Therefore, to cover a distance of 15m, J will take 15/0.5=30s
Also, to cover additional 2 m, J will take 4 s more
Total time taken=34 S
Answer D
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Re: John and Steve are speedwalkers in a race. John is 15 meters behind [#permalink]

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New post 21 Aug 2015, 12:36
2
Total distance = (15+2) metres
relative speed =0.5 m/s

final push time =17/0.5 =34 seconds
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Re: John and Steve are speedwalkers in a race. John is 15 meters behind [#permalink]

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New post 21 Aug 2015, 14:57
2
Bunuel wrote:
John and Steve are speed walkers in a race. John is 15 meters behind Steve when he begins his final push. John blazes to the finish at a pace of 4.2 m/s, while Steve maintains a blistering 3.7 m/s speed. If John finishes the race 2 meters ahead of Steve, how long was John’s final push?

A. 13 seconds
B. 17 seconds
C. 26 seconds
D. 34 seconds
E. 51 seconds

Kudos for a correct solution.


Total dist covered by John = 15+2 = 17[m]
relative speed= 4.2 - 3.7[m/s] = 0.5 [m/s]

speed = dist/time = 17/0.5 = 34 sec

D it is
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Re: John and Steve are speedwalkers in a race. John is 15 meters behind [#permalink]

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New post 21 Aug 2015, 16:48
1
John gains .5 m/s on Steve.
John needs to gain 17 meters.
17/.5 = 34 seconds
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Re: John and Steve are speedwalkers in a race. John is 15 meters behind [#permalink]

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New post 21 Aug 2015, 23:53
1
see that relative speed approach is faster

I used complicated algebra:

(15+x)/4.2=(x-2)/3.7 => x=127.8 is the distance from Steve to finish

John's time=(127.8+15)/4.2=34 sec.

D
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Re: John and Steve are speedwalkers in a race. John is 15 meters behind [#permalink]

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New post 23 Aug 2015, 11:42
1
1
Bunuel wrote:
John and Steve are speed walkers in a race. John is 15 meters behind Steve when he begins his final push. John blazes to the finish at a pace of 4.2 m/s, while Steve maintains a blistering 3.7 m/s speed. If John finishes the race 2 meters ahead of Steve, how long was John’s final push?

A. 13 seconds
B. 17 seconds
C. 26 seconds
D. 34 seconds
E. 51 seconds

Kudos for a correct solution.


Economist GMAT Tutor Official Solution:

There seems to be a lot going on here. John and Steve are both in motion, and John must overtake Steve and move ahead to the finish line. However, this problem can be simplified into a single equation.

Focus first on the rate at which the gap is being closed. The only rate you need to know to solve this problem is the rate at which John is overtaking Steve: 0.5 m/s (4.2 m/s - 3.7 m/s).

Next, treat the distance as a single unit. If we use Steve as our fixed point, we can say that John moves from -15 m (behind Steve) to 2 m (in front of Steve), or a total distance of 17 m.

Finally, calculate the time it takes to move 17 m at a speed of 0.5 m/s (time = distance/rate) to get a total of 34 seconds.

This race sounds like a nail biter, but with a little strategy, GMAT rate problems can be a walk in the park.
_________________

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?
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Re: John and Steve are speedwalkers in a race. John is 15 meters behind [#permalink]

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New post 06 Jul 2018, 10:59
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Re: John and Steve are speedwalkers in a race. John is 15 meters behind   [#permalink] 06 Jul 2018, 10:59
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