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# A motorcyclist has to cover a distance of 200 km to reach

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Manager
Joined: 25 Jan 2010
Posts: 109
Location: Calicut, India
A motorcyclist has to cover a distance of 200 km to reach [#permalink]

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16 Aug 2011, 18:46
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Difficulty:

95% (hard)

Question Stats:

15% (03:18) correct 85% (03:09) wrong based on 13 sessions

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A motorcyclist has to cover a distance of 200 km to reach city B from city A. After travelling a certain distance, his motorcycle develops a problem and travels at 3/4th of its original speed, there by he reached B 1 hour late. Had the problem developed 30 KM earlier, he would have reached b 12 mins later. Find the the initial distance traveled without the problem and the speed over that part of the journey.

A. 50KM,60KM
B. 40KM, 40KM
C. 60KM, 30KM
D. 50KM, 50 KM
E. 60KM 60KM
[Reveal] Spoiler: OA

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Joined: 20 Dec 2010
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Re: time and distance question #8 [#permalink]

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16 Aug 2011, 21:43
cleetus wrote:
A motorcyclist has to cover a distance of 200 km to reach city B from city A. After travelling a certain distance, his motorcycle develops a problem and travels at 3/4th of its original speed, there by he reached B 1 hour late. Had the problem developed 30 KM earlier, he would have reached b 12 mins later. Find the the initial distance traveled without the problem and the speed over that part of the journey.

A) 50KM,60KM
B) 40KM, 40KM
C)60KM, 30KM
D)50KM, 50 KM
E) 60KM 60KM

This is beyond GMAT because it is more laborious and less logical.

Let the initial breakdown occurred at x km
Let the initial speed be v km/h

$$\frac{x}{v}+\frac{200-x}{\frac{3}{4}v}=\frac{200}{v}+1$$ ------------------1

$$\frac{x-30}{v}+\frac{200-(x-30)}{\frac{3}{4}v}=\frac{200}{v}+1+\frac{1}{5}$$ ------------------2

Solve these equations to get x and v.

Ans: "D"
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Joined: 16 Feb 2011
Posts: 259
Re: time and distance question #8 [#permalink]

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17 Aug 2011, 06:39
um so happy to read it's beyond GMAT...wish n hope such ques nvr cum
Intern
Joined: 19 Dec 2011
Posts: 20
Re: time and distance question #8 [#permalink]

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25 Aug 2012, 12:01
A motorcyclist has to cover a distance of 200 km to reach city B from city A. After travelling a certain distance, his motorcycle develops a problem and travels at 3/4th of its original speed, there by he reached B 1 hour late. Had the problem developed 30 KM earlier, he would have reached b 12 mins later. Find the the initial distance traveled without the problem and the speed over that part of the journey.

we can use options to solve this poblem.

D) 50 KM , 50 KM

Ist part says if he travels 3/4 th of original speed he reaches 1 hour late.

3/4 th speed of 50 = 37.5

if 50 KM is already covered as in option, total time taken at reduced speed to cover remaining distance.

150 / 37.5 = 4
total time = 4 + 1 = 5

and if he has travelled at original speed , time taken
= 200/ 50 = 4

Thus, the difference = 1 hour. In all the remaining case the difference of time is not 1 hour.

Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Re: time and distance question #8 [#permalink]

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25 Aug 2012, 12:58
fluke wrote:
cleetus wrote:
A motorcyclist has to cover a distance of 200 km to reach city B from city A. After travelling a certain distance, his motorcycle develops a problem and travels at 3/4th of its original speed, there by he reached B 1 hour late. Had the problem developed 30 KM earlier, he would have reached b 12 mins later. Find the the initial distance traveled without the problem and the speed over that part of the journey.

A) 50KM,60KM
B) 40KM, 40KM
C)60KM, 30KM
D)50KM, 50 KM
E) 60KM 60KM

This is beyond GMAT because it is more laborious and less logical.

Let the initial breakdown occurred at x km
Let the initial speed be v km/h

$$\frac{x}{v}+\frac{200-x}{\frac{3}{4}v}=\frac{200}{v}+1$$ ------------------1

$$\frac{x-30}{v}+\frac{200-(x-30)}{\frac{3}{4}v}=\frac{200}{v}+1+\frac{1}{5}$$ ------------------2

Solve these equations to get x and v.

Ans: "D"

This is the advantage of multiple choice questions...)

The first equation gives $$3v+x=200.$$ The second equation boils down to $$18v+5x=1150.$$
You can try to pick the correct answer based on the first equation and even before you work out the second equation. They can't be so mean to provide more than one solution which fulfill the first equation. Or let's hope...)
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Manager
Joined: 24 Jul 2011
Posts: 76
Location: India
Concentration: Strategy, General Management
GMAT 1: 670 Q49 V33
WE: Asset Management (Manufacturing)
Re: A motorcyclist has to cover a distance of 200 km to reach [#permalink]

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27 Aug 2012, 08:28
2
KUDOS
Why not solve this problem in different way ?

Distance................: A...............................................B
Velocity..................: V...............l....3V/4..................... (this takes +1 hr)
If 30 KM before......: V.........l..........3V/4............................ (this takes +1 hr + 12 minutes)

So, we can deduce that as the cyclist lowered the speed from V to 3V/4 to cover 30 KM, he tool 12 minutes more time.

So, forming equation to find the difference of time we get we get

$$30*4/3V - 30/V = 12$$
$$=> 40/V - 30/V=12$$
$$=> 10/V=12$$
$$=> V=10 KM/12 Minutes$$
$$=> V=50 KM/Hr$$

Only option D has this value. So, it is the right answer
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Joined: 06 Sep 2013
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Re: A motorcyclist has to cover a distance of 200 km to reach [#permalink]

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26 Nov 2013, 12:52
cleetus wrote:
A motorcyclist has to cover a distance of 200 km to reach city B from city A. After travelling a certain distance, his motorcycle develops a problem and travels at 3/4th of its original speed, there by he reached B 1 hour late. Had the problem developed 30 KM earlier, he would have reached b 12 mins later. Find the the initial distance traveled without the problem and the speed over that part of the journey.

A. 50KM,60KM
B. 40KM, 40KM
C. 60KM, 30KM
D. 50KM, 50 KM
E. 60KM 60KM

This is not GMAT material
Cheers
J
Re: A motorcyclist has to cover a distance of 200 km to reach   [#permalink] 26 Nov 2013, 12:52
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