Time & Distance - Source : Maths Tough problems

[jitendra_mulchandani]

54. Two people walked the same distance, one person's speed is between 25 and 45,and if he used 4 hours, the speed of another people is between 45 and 60,and if he used 2 hours, how long is the distance?
A.116
B.118
C.124
D.136
E.140

Solution: Considering the speed of the two persons.

---------------------------
First Approach
---------------------------
Distance traveled within 4 hours will be within the range
= 25*4 - 45*4
=100 - 180

Second person -
Distance traveled within 2 hours will be within the range
= 45*2 - 60*2
=90 - 120

Options A and B satisfy these conditions

---------------------------
Second Approach
---------------------------
First person -
=average speed*hours travelled
= (2*V1*V2) / V1 + V2
=128.5

Similarly, for second person:
~103

To decide between the options, I just took out the average of these two values.

=129 + 103 / 2 = 116

I am just wondering whether taking out the average of the two values is the correct thing to do....

[kstv]

Person X's speed is 25 to 45 and takes 4 hrs so distance is between 100 to 180
Person Y's speed is 45 to 60 and takes 2 hrs distance is between 90 to 120
The distance has to be in the range 100 to 120 as it is same fro X and Y
Option A and B
Y's speed 116/2 = 58
Y covers it in half the time so his speed is double of X
Possible value of his speed is 50 to 60
X's speed 29 116/29 is not 4 hrs

if the distance is 118
Y's speed 118/2 = 59
X's speed is 59/2 Time = (118/59)*2 = 4

IMO B

[sanju09]

54. Two people walked the same distance, one person's speed is between 25 and 45,and if he used 4 hours, the speed of another people is between 45 and 60,and if he used 2 hours, how long is the distance?
A.116
B.118
C.124
D.136
E.140

Solution: Considering the speed of the two persons.

---------------------------
First Approach
---------------------------
Distance traveled within 4 hours will be within the range
= 25*4 - 45*4
=100 - 180

Second person -
Distance traveled within 2 hours will be within the range
= 45*2 - 60*2
=90 - 120

Options A and B satisfy these conditions

---------------------------
Second Approach
---------------------------
First person -
=average speed*hours travelled
= (2*V1*V2) / V1 + V2
=128.5

Similarly, for second person:
~103

To decide between the options, I just took out the average of these two values.

=129 + 103 / 2 = 116

I am just wondering whether taking out the average of the two values is the correct thing to do....

I am totally clueless about your second approach; leave alone my approval for it. Even kstv did it in panic to exclude one choice, see

X's speed 29 116/29 is not 4 hrs

Can't say why the wordings are not having GMATesque sound, but it sounds like a greatly flawed question in the end.

If x long is the distance each of the two traveled, then we have two intervals available for x

100 < x < 180 and also that 90 < x < 120,

and this reduces the optimum interval to 100 < x < 120.

We are really lucky that we need to check at most two choices that fall in the said interval, those are A & B.

The best clue in the stem is that one guy is twice as fast as the other, so let's check which of the two choices prove it holds. In fact all choices within the optimum interval of 100 < x < 120 are correct.

AMBIGUOUS

I am finding it really hard to reach a source called "Maths Tough problems".

[kstv]

The option should have included only 116 or 118 or any one value between 100 to 120. Then it is O.K. Source of this problem ?

[jitendra_mulchandani]

This is the source....
https://www.beatthegmat.com/difficult-gm ... s-t78.html

For second approach, I was trying to find out the average speed and then get close to one of the options - 116 or 118.

But, kstv's approach is correct.

Thanks kstv

[sanju09]

This is the source....
https://www.beatthegmat.com/difficult-gm ... s-t78.html

For second approach, I was trying to find out the average speed and then get close to one of the options - 116 or 118.

But, kstv's approach is correct.

Thanks kstv

It's really a very polite gesture to thank somebody, but never tame any misunderstanding.

[ArunangsuSahu]

Just go by options..divide by 4 and 2 to match the two ranges

[[email protected]]

Its 116...
Explanation:
Speed of A=A
Speed of B=B

=> A*4=B*2
=>2A=B.

Now for A=29, B=58.
Distance=29*4=116=58*4.

This is the only options that satisfies the above result.