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M04 Q21 - soccer coach bike ride

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Intern
Intern
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Joined: 09 Jul 2013
Posts: 19
Location: United States
Schools: Wharton '17, Haas '17
GMAT 1: 710 Q44 V44
GMAT 2: Q V
GPA: 3.65
WE: Military Officer (Military & Defense)
Followers: 0

Kudos [?]: 11 [0], given: 10

Re: M04 Q21 - soccer coach bike ride [#permalink] New post 16 Oct 2013, 08:28
A.

A good place to start is with organizing the given information into a Distance = Rate x Time chart.

D = R x T

We are trying to find D, the distance. We are given a set of clues to include the coach's rate of travel and variations of rate and time for the same distance.

We know that the dude is traveling at 24 km/hr.

D = R x T
?? = 24 x ??

We know that he was 5 minutes late. Let T = time in minutes. T+5.
D = R x T
?? = 24 x (T+5)

We know that if he traveled 25% faster (1 + 25/100 = 125/100 or 125%), he would be 4 minutes early (T-4). Make a new line in your chart.
D = R x T
?? = 24 x (T+5)
?? = 24(125%) x (T-4)

Here it would be useful to convert everything into the same units (minutes not hours). 24 k/hr converted into kilometers/minute = 24k/60min = 2km/5min. Also, 125% of 2/5 is 1/2.

Now you have (Let D = the distance the coach traveled):
D = R x T
D = 2/5 x (T+5)
D = 1/2 x (T-4)

Since the distance is the same in both the late and the early scenarios, you can set the equations equal to each other and solve for Time, your only variable.
2/5 x (T+5) = 1/2 x (T-4)
Which gives you T = 40 minutes.

Plug 40 minutes into either equation to find the Distance.
D = 2/5 x (40+5)
D = 18 km.
And this is the answer.

Long algebraic way to do it, I'm sure there are more efficient ways.
Intern
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Joined: 13 Aug 2013
Posts: 23
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Kudos [?]: 3 [0], given: 1

Re: M04 Q21 - soccer coach bike ride [#permalink] New post 17 Oct 2013, 02:18
An increase in speed by 25% means reduction in time by 20% (percentage change graphic) which is 9. so actual time is 9x5=45 mins. At the speed of 24km/hr, time taken to reach is 3/4 hrs. hence distance = 24x3/4 =18km (A one-liner if you'r through with the basics of percentages)
Re: M04 Q21 - soccer coach bike ride   [#permalink] 17 Oct 2013, 02:18
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