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sgr21: Junior | Next Rank: 30 Posts; Posts: 28; Joined: Mon Oct 21, 2013 12:52 am

by sgr21 » Mon Oct 21, 2013 10:51 am

A man completes a journey in 40 hours. He travels half of the journey's distance at the rate of 84 km/hr and the other half of the journey's distance at the rate of 96 km/hr. Find the total distance that the man covered during the journey?
(A)448 km
(B) 1792 km
(C) 896 km
(D)908 km

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Source: Beat The GMAT — Problem Solving | Mon Oct 21, 2013 10:51 am

theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Mon Oct 21, 2013 11:40 am

Let total distance be "x".
Total time = Time of split1 + Time of Split2
40 = (x/2)/84 + (x/2)/96

40*2 = x (1/84 + 1/96)

x = 80 * 96 * 84 / (96+84)
= 3584

Are you sure of the answer choices?

R A H U L

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rakeshd347: Master | Next Rank: 500 Posts; Posts: 391; Joined: Sat Mar 02, 2013 5:13 amFollowed by: 4 members; Thanked: 50 times

by rakeshd347 » Mon Oct 21, 2013 12:06 pm

sgr21 wrote:A man completes a journey in 40 hours. He travels half of the journey's distance at the rate of 84 km/hr and the other half of the journey's distance at the rate of 96 km/hr. Find the total distance that the man covered during the journey?
(A)448 km
(B) 1792 km
(C) 896 km
(D)908 km

Hi Mate,

As Rahul has mentioned that these answer choices are wrong. I think they are definitely wrong dude. He finished a 40 hours journey at the speed of 84 and 96. We can calculate the distance but it will be no where near to the answer choices why? Because even if the man would have travelled at the speed of 84km/hour for the whole journey he would have covered more than 3200km. If he would have covered the whole journey and not half with the speed of 96km/h then the distance he would have covered would be more than 3800. So the right answer will be between these two numbers. There is no way answer can be anywhere near to these. Because answer doesn't mention that the man stopped and took rest for 30 hours or so. He has been walking whole time with these speeds.

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AIM TO CRACK GMAT: Senior | Next Rank: 100 Posts; Posts: 80; Joined: Sat Sep 15, 2012 1:07 amFollowed by: 1 member; Thanked: 1 times

by AIM TO CRACK GMAT » Mon Oct 21, 2013 12:20 pm

heyguys... i chkd the question...d source is SPJAT.. n d OA is B

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rakeshd347: Master | Next Rank: 500 Posts; Posts: 391; Joined: Sat Mar 02, 2013 5:13 amFollowed by: 4 members; Thanked: 50 times

by rakeshd347 » Mon Oct 21, 2013 2:53 pm

AIM TO CRACK GMAT wrote:heyguys... i chkd the question...d source is SPJAT.. n d OA is B

I am really suspected on the OA. first, this question has never been discussed in any forum. Second let us say that OA is B for argument sake.
So the total distance is 1792.
So the man covered 896km at the speed of 84km/hr and 896 at the speed of 96km/hour.

So total time taken while travelling at 84km/hr=896/84>10.40 ( roughly little more than 10 hours)
Time taken while travelling at 96km/hr=896/96<10 hours.
So the total time taken by the man is 20hours (round about that range).

So where did 40hours go? what did the man do in the rest of the 20 hours.

I would throw this source because not only the question doesn't make sense but also never heard of this source.

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Mon Oct 21, 2013 6:38 pm

Yeah, I agree with Rakesh... OA cannot be {B}..

As, if we suppose speed as "84",which is the minimum of the speeds, then distance traveled in 40 hours
= 84*40 = 3360km

For it to be 1792, the speed should have been ~45km/h.. that's not the case

R A H U L

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Wed Oct 23, 2013 3:10 am

sgr21 wrote:A man completes a journey in 40 hours. He travels half of the journey's distance at the rate of 84 km/hr and the other half of the journey's distance at the rate of 96 km/hr. Find the total distance that the man covered during the journey?
(A)448 km
(B) 1792 km
(C) 896 km
(D)908 km

You picked a wrong source for a GMAT question. Such sources are very dangerous for GMAT preparation. Please be careful and always chose the right source before choosing a good question there.

A Rule:

In the cases where half of the journey is traveled at x speed and the remaining half of the journey is traveled at y speed, the average speed happens to be 2xy/ (x + y).

Hence, in the present case, average speed =

2(84)(96)/ (84 + 96) = 2(28)(8)/5

The total time taken = 40

Hence, total distance traveled = [2(28)(8)/5] (40) = 2(28)(8)(8) = 3584

It's nowhere in the four answers. I am sure the missing fifth carried the right answer, but that's missing.

Few signs that the source is vague:

"¢ Answers not in order.
"¢ GMAT prefers to give name(s) to the person(s) in question, instead calling them " A man or A woman", as it sounds a bit disrespectful about the person in question.
"¢ Distances are preferably in miles than in kilometres.
"¢ Etc.

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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anchalmathur01: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Tue Jul 22, 2014 2:00 pm

by anchalmathur01 » Tue Jul 22, 2014 2:07 pm

Hello All,

I think the question posted here is wrong, the total time is 20 Hrs.

We all know the formula for Distance = Speed * Time, Hence we will use this formula to solve the sum.

First we will calculate the average speed, for which we know the formula :

(2xy/x+y), hence here it will be (2*84*96/84 + 96) ,

we will now put the values in the formula, hence we get:

Distance = [ (2* 84*96/ 180) * 20]
Distance = 1792 Km

Thanks,
Anchal Mathur

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Tue Jul 22, 2014 8:31 pm

anchalmathur01 wrote:Hello All,

I think the question posted here is wrong, the total time is 20 Hrs.

We all know the formula for Distance = Speed * Time, Hence we will use this formula to solve the sum.

First we will calculate the average speed, for which we know the formula :

(2xy/x+y), hence here it will be (2*84*96/84 + 96) ,

we will now put the values in the formula, hence we get:

Distance = [ (2* 84*96/ 180) * 20]
Distance = 1792 Km

Thanks,
Anchal Mathur

Hi Anchal,

The question is Definitely INCORRECT and it can be solved this way

If Total Distance = 2D
Time taken to cover first half the distance D = Distance/Speed = D/84
Time taken to cover second half the distance D = Distance/Speed = D/96

Total Time = 40 Hrs. = (D/84) + (D/96)
(8D+7D)/(12x7x8) = 40
15D = 40x12x7x8
D = 40x12x7x8/15 = 1792

Therefore total Distance = 1792 x 2 = 3584 KM

If the Question were what is the Half way distance then

Answer: Option B

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