Time,Speed & Distance

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 am; Thanked: 230 times; Followed by:21 members

Time,Speed & Distance

by shankar.ashwin » Sun Sep 11, 2011 6:24 am

2 people A and B at opposite end of a road start walking towards each other at 10:00 a.m; they meet together at 11:20 a.m, A reaches the end of the road (point where B had begun) 2 hrs before B reaches the other end. Find the total time taken for travel of the entire journey by A.

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Source: Beat The GMAT — Problem Solving | Sun Sep 11, 2011 6:24 am

cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 am; Location: India; Thanked: 310 times; Followed by:123 members; GMAT Score:750

by cans » Sun Sep 11, 2011 9:11 am

time taken to meet = 80 min.
let A in x hr, then B in x+2...
I think some info is missing in this question....

If my post helped you- let me know by pushing the thanks button

Contact me about long distance tutoring!
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Cans!!

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saketk: Legendary Member; Posts: 608; Joined: Sun Jun 19, 2011 11:16 am; Thanked: 37 times; Followed by:8 members

by saketk » Sun Sep 11, 2011 11:07 am

shankar.ashwin wrote:2 people A and B at opposite end of a road start walking towards each other at 10:00 a.m; they meet together at 11:20 a.m, A reaches the end of the road (point where B had begun) 2 hrs before B reaches the other end. Find the total time taken for travel of the entire journey by A.

this is an incomplete question.

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abhimanyu.tanwar: Senior | Next Rank: 100 Posts; Posts: 55; Joined: Wed Sep 22, 2010 9:09 am; Location: Pune, India; Thanked: 1 times

by abhimanyu.tanwar » Tue Sep 13, 2011 10:02 am

is the answer 2 hours?

Regards
Abhimanyu

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saketk: Legendary Member; Posts: 608; Joined: Sun Jun 19, 2011 11:16 am; Thanked: 37 times; Followed by:8 members

by saketk » Wed Sep 14, 2011 12:26 pm

abhimanyu.tanwar wrote:is the answer 2 hours?

Question is incomplete. You cannot find the answer with the information provided.

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pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pm; Thanked: 158 times; Followed by:21 members

by pemdas » Wed Sep 14, 2011 1:44 pm

time unit is an hour
distance = d
cross point time = 4/3
times: A=B-2
speeds: d/(B-2), d/B
[spoiler]combined speed: 2d(B-1)/B(B-2)[/spoiler]
equation => 4/3*[d/(B-2)+d/B]=d, 8d(B-1)/3B(B-2)=d, 8(B-1)/3B(B-2)=1, 8(B-1)=3B(B-2), 8B-8=3B^2-6B, 3B^2-14B+8=0, B(1,2)=[14 +- sqroot(196-96)]/6, B(1,2)=(14 +- 10)/6 <> (2/3;4)

since cross point time was 4/3 the time spent by B cannot be 2/3 (ignore). Admit 4. Time spent by A is (4-2)=2 hours

2 hours is my answer

shankar.ashwin wrote:2 people A and B at opposite end of a road start walking towards each other at 10:00 a.m; they meet together at 11:20 a.m, A reaches the end of the road (point where B had begun) 2 hrs before B reaches the other end. Find the total time taken for travel of the entire journey by A.

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Proleefeek: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Fri Aug 05, 2011 6:49 pm

by Proleefeek » Wed Sep 14, 2011 5:35 pm

@ Pemdas

4/3*[d/(B-2)+d/B]=d

This equation is incorrect. On the RHS you have a distance unit on the LHS you have a Speed unit. Kindly re-evaluate your equation.

IMO the problem definitely lacks information.

let us assume, A travels at avg speed 'a' and B travels at avg speed 'b'. Since nothing is mentioned about the relative velocities of these two individuals we assume (a,b) to remain constant.

At 4/3 hrs, they meet.

Thus total distance of journey = 4/3*(a+b)
Now lets say A completes his journey in t1 time. thus B will have completed his in t1+2 hrs.
Since we are aware of Total Distance and assumed A's speed to be a we can formulate the total time taken by A to complete the journey, which is:

t1 = 4/3*(a+b)/a
= 4/3 +4/3*(b/a)

Since no ratio is provided to correlate both the speeds, we are lacking that info. Notice that if it was mentioned that B completes his journey in 2t1 as opposed to t1+2 then we could have determined t1 as t1 = 4/3 + 4/3*1/2 = 4/3+2/3 = 6/3 = 2hrs.

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 am; Thanked: 230 times; Followed by:21 members

by shankar.ashwin » Wed Sep 14, 2011 8:49 pm

Guys apologies. There was a small mistake in the way I interpreted the problem.
This problem does have some data missing to determine a finite solution.

Now try this,

2 people A and B at opposite end of a road start walking towards each other at 10:00 a.m; they meet together at 11:20 a.m, Had A and B begun their journey at the same point at the same time, A would have reached the end of the road 2 hrs before B did. Find the total time taken for travel of the entire journey by A.

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saketk: Legendary Member; Posts: 608; Joined: Sun Jun 19, 2011 11:16 am; Thanked: 37 times; Followed by:8 members

by saketk » Wed Sep 14, 2011 10:31 pm

shankar.ashwin wrote:Guys apologies. There was a small mistake in the way I interpreted the problem.
This problem does have some data missing to determine a finite solution.

Now try this,

2 people A and B at opposite end of a road start walking towards each other at 10:00 a.m; they meet together at 11:20 a.m, Had A and B begun their journey at the same point at the same time, A would have reached the end of the road 2 hrs before B did. Find the total time taken for travel of the entire journey by A.

Hey,

Can you please tell me what is the source of this question ?

this question also does not have any absolute answer..

let me explain:- let the total distance between A and B is equal to x.

As per second part of the question-- If A takes 't' hours to complete X miles
then 'B' will take 't+2' hrs.

A's speed = x/t miles/hr
B's speed = x/(t+2) miles/hr

now let's go to first part of the question -

A and B meets at 11.20 am i.e after 1 hr 20 mins

or after 4/3 hrs

Distance covered by A = 4/3*(x/t)
Distance covered by B = 4/3*[x/(t+2)] -- this is the distance which A will have to cover

x/t hrs ---- 4/3 hrs
[x/(t+2)] ---- 4/3*(t/x)*[x/(t+2)] hrs
or ---------- 4/3*t/(t+2) hrs

Therefore total time taken by A to cover X miles--

4/3+ 4/3*t/(t+2) hrs

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eshwarjayanth: Senior | Next Rank: 100 Posts; Posts: 40; Joined: Mon Oct 18, 2010 8:32 am

by eshwarjayanth » Wed Sep 14, 2011 10:42 pm

shankar.ashwin wrote:Guys apologies. There was a small mistake in the way I interpreted the problem.
This problem does have some data missing to determine a finite solution.

Now try this,

2 people A and B at opposite end of a road start walking towards each other at 10:00 a.m; they meet together at 11:20 a.m, Had A and B begun their journey at the same point at the same time, A would have reached the end of the road 2 hrs before B did. Find the total time taken for travel of the entire journey by A.

starting from opp points: Taking the time in mins
a = rate of A
b = rate of B
when they meet at 11:20am (80 mins from start time) they both must have covered the entire distance D
so D = 80a + 80b => D = 80(a+b) ---> eq1

starting from same points: Taking time in mins
let time taken by B to cover distance D be x mins
so time taken by A ot cover D is x-120 mins (given, A would have reached the end of the road 2 hrs before B did)
So D = bx ---> eq2
& D = a(x-120) ---> eq3
from 1 & 2, b = (80a)/(x-80)
1 & 3, a(x-120) = 80b
subs b in above eq => x = 40mins or 240mins
40mins does not satisfy, so 240mins or 4hrs is the ans.

please let me know if this is the correct ans

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 am; Thanked: 230 times; Followed by:21 members

by shankar.ashwin » Wed Sep 14, 2011 11:15 pm

The OA is 2 hrs

My soln;

Let speed of A = s1
speed of B = s2
Total time taken by A = t
Distance between 2 points = d

s1 * t = d .... (1)
s2 * (t+2) = d ..... (2)
(s1 + s2) 4/3 = d ....(3) [Both would have covered the total distance when they meet after 1hr 20 mins]

From (1) and (3)

s1*t = (s1+s2) 4/3
s1(3t-4) = 4s2 ......(4)

From (2) and (3)

4s1=s2(2+3t) .......(5)

From (4) and (5)

4/(3t-4) = (2+3t)/4

3t^2 - 2t - 8 = 0

t = -4/3 (or) 2

So time taken by A = t = 2hrs.
Time taken by B = t+2 = 4hrs.

I guess its a fairly difficult problem, maybe 750+

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pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pm; Thanked: 158 times; Followed by:21 members

by pemdas » Thu Sep 15, 2011 1:51 am

@Proleefeek, on the right hand side I have a distance, that's correct.
on the left hand side I also have a distance. When A and B cover small distances towards each other, they will meat at some point and will definitely cover ONE whole distance upon the time of cross point, AGREE?

So, on the LHS and RHS is the same value - distance.

p.s. before judging a solution as correct or incorrect, plz weigh all pros and cons

Proleefeek wrote:@ Pemdas

4/3*[d/(B-2)+d/B]=d

This equation is incorrect. On the RHS you have a distance unit on the LHS you have a Speed unit. Kindly re-evaluate your equation.

IMO the problem definitely lacks information.

let us assume, A travels at avg speed 'a' and B travels at avg speed 'b'. Since nothing is mentioned about the relative velocities of these two individuals we assume (a,b) to remain constant.

At 4/3 hrs, they meet.

Thus total distance of journey = 4/3*(a+b)
Now lets say A completes his journey in t1 time. thus B will have completed his in t1+2 hrs.
Since we are aware of Total Distance and assumed A's speed to be a we can formulate the total time taken by A to complete the journey, which is:

t1 = 4/3*(a+b)/a
= 4/3 +4/3*(b/a)

Since no ratio is provided to correlate both the speeds, we are lacking that info. Notice that if it was mentioned that B completes his journey in 2t1 as opposed to t1+2 then we could have determined t1 as t1 = 4/3 + 4/3*1/2 = 4/3+2/3 = 6/3 = 2hrs.