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
dist
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- theCodeToGMAT
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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?
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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Hi Mate,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
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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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.AIM TO CRACK GMAT wrote:heyguys... i chkd the question...d source is SPJAT.. n d OA is B
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.
- theCodeToGMAT
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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
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
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- sanju09
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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.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
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.
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- anchalmathur01
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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
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
- GMATinsight
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Hi Anchal,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
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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