speed distance--very hard

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quantskillsgmat: Senior | Next Rank: 100 Posts; Posts: 96; Joined: Fri Apr 23, 2010 1:14 amFollowed by: 1 member; Thanked: 1 times

by quantskillsgmat » Sat Sep 17, 2011 1:07 am

two buses c and d are operated between cities m and n .one day c and d started from m and n respectively towards n and m respectively.after 2 buses cross each other, the bus c takes 5 hrs to reach city n and d takes 3 hrs 12 minutes to reach city m.after how much time from the start did c and d cross each other.
a)4 hrs 24 minutes
b)4 hrs 6 minutes
c)4 hrs 18 minutes
d)4 hrs

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Source: Beat The GMAT — Problem Solving | Sat Sep 17, 2011 1:07 am

aplavakarthik: Senior | Next Rank: 100 Posts; Posts: 56; Joined: Thu Jul 07, 2011 2:16 am; Thanked: 2 times

by aplavakarthik » Sat Sep 17, 2011 2:23 am

r v missing anything in the question?

it say jus c took 5 more hours from the meet point and D took 3.12 hours from the meet point. One thing for sure is they are not travelling at same speed( if they did start at the same time). so the time it took for C will be different from the time it took for D to reach the meeting point..........

so I have no clues to proceed further.......

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sl750: Master | Next Rank: 500 Posts; Posts: 496; Joined: Tue Jun 07, 2011 5:34 amFollowed by: 1 member; Thanked: 38 times

by sl750 » Sat Sep 17, 2011 2:31 am

at the time the buses cross each other, the time is the same

s1-speed of bus1; s2 speed of bus2. total distance is d
t(s1+s2)=d ---1

total time taken by bus a is t+5 hrs. Therefore,

s1=d/t+5. Similarly, total time taken by bus B is t+3.2 hrs
s2=d/t+3.2

Substitute the values of s1 and s2 in the first equation

t(t+3.2+t+5)=(t+5)(t+3.2)

Solving, we get t=4hrs

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aplavakarthik: Senior | Next Rank: 100 Posts; Posts: 56; Joined: Thu Jul 07, 2011 2:16 am; Thanked: 2 times

by aplavakarthik » Sat Sep 17, 2011 2:54 am

sl750 wrote:at the time the buses cross each other, the time is the same

s1-speed of bus1; s2 speed of bus2. total distance is d
t(s1+s2)=d ---1

total time taken by bus a is t+5 hrs. Therefore,

s1=d/t+5. Similarly, total time taken by bus B is t+3.2 hrs
s2=d/t+3.2

Substitute the values of s1 and s2 in the first equation

t(t+3.2+t+5)=(t+5)(t+3.2)

Solving, we get t=4hrs

time taken by bus a and b cannot be considered the t+5 and t+3.12, t cannot be the same. time taken by both a and b are different. t1+5,t2+3.2

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Sep 17, 2011 3:12 am

quantskillsgmat wrote:two buses c and d are operated between cities m and n .one day c and d started from m and n respectively towards n and m respectively.after 2 buses cross each other, the bus c takes 5 hrs to reach city n and d takes 3 hrs 12 minutes to reach city m.after how much time from the start did c and d cross each other.
a)4 hrs 24 minutes
b)4 hrs 6 minutes
c)4 hrs 18 minutes
d)4 hrs

We can plug in the answers, which represent the time for C and D to meet.
We should start with the only answer choice that offers an integer value.

Answer choice D: 4 hours for C and D to meet.
Since C requires 5 more hours to reach its destination, the total time for C = 4+5 = 9 hours.
Since D requires 16/5 hours to reach its destination, the total time for D = 4 + 16/5 = 36/5 hours.
Let distance = 36 miles.
Rate for C = d/t = 36/9 = 4 miles per hour.
Rate for D = d/t = 36/(36/5) = 5 miles per hour.
Combined rate for C and D when they travel toward each other = 4+5 = 9 miles per hour.
Time for C and D to meet = d/r = 36/9 = 4 hours.
Success!

The correct answer is D.

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sl750: Master | Next Rank: 500 Posts; Posts: 496; Joined: Tue Jun 07, 2011 5:34 amFollowed by: 1 member; Thanked: 38 times

by sl750 » Sat Sep 17, 2011 5:50 am

aplavakarthik wrote:
sl750 wrote:at the time the buses cross each other, the time is the same

s1-speed of bus1; s2 speed of bus2. total distance is d
t(s1+s2)=d ---1

total time taken by bus a is t+5 hrs. Therefore,

s1=d/t+5. Similarly, total time taken by bus B is t+3.2 hrs
s2=d/t+3.2

Substitute the values of s1 and s2 in the first equation

t(t+3.2+t+5)=(t+5)(t+3.2)

Solving, we get t=4hrs
time taken by bus a and b cannot be considered the t+5 and t+3.12, t cannot be the same. time taken by both a and b are different. t1+5,t2+3.2

t is the time when the two buses meet. Their total times are not the same

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gmatboost: Master | Next Rank: 500 Posts; Posts: 312; Joined: Tue Aug 02, 2011 3:16 pmFollowed by: 33 members; Location: New York City; Thanked: 130 times; GMAT Score:780

by gmatboost » Sat Sep 17, 2011 8:29 pm

I like the approach by sl750. Another approach

Call the distance C covers first (up to the meeting point) X and the distance C covers second Y.

C covers Y in 5 hours. Rate: Y/5.
D covers X in 3 1/5 = 16/5 hours. Rate: X/(16/5) = 5X/16.

C covers X in the same time that D covers Y. Use time = distance/rate
X / (Y/5) = Y / (5X/16)
5X/Y = 16Y/5X
25X^2 = 16Y^2
5X = 4Y

C covers Y in 5 hours.
C covers 5X/4 in 5 hours.
C covers X in (4/5) * 5 hours = 4 hours.

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DonPaw: Junior | Next Rank: 30 Posts; Posts: 27; Joined: Sat May 01, 2010 7:57 pm

by DonPaw » Tue Sep 27, 2011 8:38 pm

GMATGuruNY wrote:
quantskillsgmat wrote:two buses c and d are operated between cities m and n .one day c and d started from m and n respectively towards n and m respectively.after 2 buses cross each other, the bus c takes 5 hrs to reach city n and d takes 3 hrs 12 minutes to reach city m.after how much time from the start did c and d cross each other.
a)4 hrs 24 minutes
b)4 hrs 6 minutes
c)4 hrs 18 minutes
d)4 hrs
We can plug in the answers, which represent the time for C and D to meet.
We should start with the only answer choice that offers an integer value.

Answer choice D: 4 hours for C and D to meet.
Since C requires 5 more hours to reach its destination, the total time for C = 4+5 = 9 hours.
Since D requires 16/5 hours to reach its destination, the total time for D = 4 + 16/5 = 36/5 hours.
Let distance = 36 miles.
Rate for C = d/t = 36/9 = 4 miles per hour.
Rate for D = d/t = 36/(36/5) = 5 miles per hour.
Combined rate for C and D when they travel toward each other = 4+5 = 9 miles per hour.
Time for C and D to meet = d/r = 36/9 = 4 hours.
Success!

The correct answer is D.

Mitch,

I'm big fan of your reasoning and answering style. I try to think any problem as how you possibly would see and I'm getting success.

I need your help in this particular problem where you picked 4 as option and solved it quickly.what if I pick other options and try to solve within 2 mins.. it will take too much time.. can you suggest how to think ..

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Sep 28, 2011 3:13 am

DonPaw wrote:
GMATGuruNY wrote:
quantskillsgmat wrote:two buses c and d are operated between cities m and n .one day c and d started from m and n respectively towards n and m respectively.after 2 buses cross each other, the bus c takes 5 hrs to reach city n and d takes 3 hrs 12 minutes to reach city m.after how much time from the start did c and d cross each other.
a)4 hrs 24 minutes
b)4 hrs 6 minutes
c)4 hrs 18 minutes
d)4 hrs
We can plug in the answers, which represent the time for C and D to meet.
We should start with the only answer choice that offers an integer value.

Answer choice D: 4 hours for C and D to meet.
Since C requires 5 more hours to reach its destination, the total time for C = 4+5 = 9 hours.
Since D requires 16/5 hours to reach its destination, the total time for D = 4 + 16/5 = 36/5 hours.
Let distance = 36 miles.
Rate for C = d/t = 36/9 = 4 miles per hour.
Rate for D = d/t = 36/(36/5) = 5 miles per hour.
Combined rate for C and D when they travel toward each other = 4+5 = 9 miles per hour.
Time for C and D to meet = d/r = 36/9 = 4 hours.
Success!

The correct answer is D.

Mitch,

I'm big fan of your reasoning and answering style. I try to think any problem as how you possibly would see and I'm getting success.

I need your help in this particular problem where you picked 4 as option and solved it quickly.what if I pick other options and try to solve within 2 mins.. it will take too much time.. can you suggest how to think ..

I'm glad that you've been finding my strategies helpful.
I view the math section of the GMAT less as a math test than as a REASONING test.

The GMAT tends to use pretty numbers.
In a problem about rate and time, the correct number of minutes will almost certainly be a factor of 60: 6, 12, 15, 20, etc.

In A, 24 minutes is not a factor of 60.
In C, 18 minutes is not a factor of 60.
When the 6 minutes in B are added onto D's time of 3 hours and 12 minutes, the sum will include a time of 18 minutes, which is not a factor of 60.
There is little very chance that A, B or C would be the correct answer here.

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DonPaw: Junior | Next Rank: 30 Posts; Posts: 27; Joined: Sat May 01, 2010 7:57 pm

by DonPaw » Wed Sep 28, 2011 6:08 am

GMATGuruNY wrote:
DonPaw wrote:
GMATGuruNY wrote:
quantskillsgmat wrote:two buses c and d are operated between cities m and n .one day c and d started from m and n respectively towards n and m respectively.after 2 buses cross each other, the bus c takes 5 hrs to reach city n and d takes 3 hrs 12 minutes to reach city m.after how much time from the start did c and d cross each other.
a)4 hrs 24 minutes
b)4 hrs 6 minutes
c)4 hrs 18 minutes
d)4 hrs
We can plug in the answers, which represent the time for C and D to meet.
We should start with the only answer choice that offers an integer value.

Answer choice D: 4 hours for C and D to meet.
Since C requires 5 more hours to reach its destination, the total time for C = 4+5 = 9 hours.
Since D requires 16/5 hours to reach its destination, the total time for D = 4 + 16/5 = 36/5 hours.
Let distance = 36 miles.
Rate for C = d/t = 36/9 = 4 miles per hour.
Rate for D = d/t = 36/(36/5) = 5 miles per hour.
Combined rate for C and D when they travel toward each other = 4+5 = 9 miles per hour.
Time for C and D to meet = d/r = 36/9 = 4 hours.
Success!

The correct answer is D.

Mitch,

I'm big fan of your reasoning and answering style. I try to think any problem as how you possibly would see and I'm getting success.

I need your help in this particular problem where you picked 4 as option and solved it quickly.what if I pick other options and try to solve within 2 mins.. it will take too much time.. can you suggest how to think ..
I'm glad that you've been finding my strategies helpful.
I view the math section of the GMAT less as a math test than as a REASONING test.

The GMAT tends to use pretty numbers.
In a problem about rate and time, the correct number of minutes will almost certainly be a factor of 60: 6, 12, 15, 20, etc.

In A, 24 minutes is not a factor of 60.
In C, 18 minutes is not a factor of 60.
When the 6 minutes in B are added onto D's time of 3 hours and 12 minutes, the sum will include a time of 18 minutes, which is not a factor of 60.
There is little very chance that A, B or C would be the correct answer here.

what to say !! simply superb !!

I guess GMAT makers also realize that these kind of problems can take more time .. but how effectively we analyse rather solve mathematically makes the difference. Thanks once again Mitch.. you are gem ..

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