rate problem

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finance: Master | Next Rank: 500 Posts; Posts: 150; Joined: Tue Mar 08, 2011 4:38 am; Thanked: 5 times

by finance » Mon Jul 18, 2011 4:28 am

Two cars A and B start from Boston and New York respectively simultaneously and travel towards each other at constant speeds along the same route. After meeting at a point between Boston and New York the two cars A and B proceed to their respective destinations of New York and Boston. Car A reaches New York 40 minutes after the two cars have met and Car B reaches Boston 90 minutes after they have met. How long did Car A take to cover the distance between Boston and New York?

A. 1 hour

B. 1 hour 10 minutes

C. 2 hours 30 minutes

D. 1 hour 40 minutes

E. 2 hours 10 minutes

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Source: Beat The GMAT — Problem Solving | Mon Jul 18, 2011 4:28 am

amit2k9: Master | Next Rank: 500 Posts; Posts: 461; Joined: Tue May 10, 2011 9:09 amFollowed by: 3 members; Location: pune; Thanked: 36 times

by amit2k9 » Mon Jul 18, 2011 6:43 am

t be the time when A and B meet up.
d be the total distance between the two cities.
A and B be the individual speeds.

thus, At+ Bt = d
also, At+ 2/3* A = d
and Bt+3/2* B = d

thus, At+Bt = At+2/3 * A gives Bt = 2/3*A
and At+Bt = Bt+3/2*B gives At = 3/2 * B

hence, At = A/t * 2/3 * 3/2 gives t=1.

thus total time for A is 1hr +40 mins.

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newgmattest: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Wed May 18, 2011 8:48 pm; Thanked: 4 times

by newgmattest » Mon Jul 18, 2011 9:15 pm

Any help on this please?

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finance: Master | Next Rank: 500 Posts; Posts: 150; Joined: Tue Mar 08, 2011 4:38 am; Thanked: 5 times

by finance » Mon Jul 18, 2011 10:42 pm

amit2k9 wrote:
also, At+ 2/3* A = d
and Bt+3/2* B = d

I didn't get this part. What is 2/3*A?? How did you find 3/2 * B??

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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 » Tue Jul 19, 2011 2:52 am

finance wrote:Two cars A and B start from Boston and New York respectively simultaneously and travel towards each other at constant speeds along the same route. After meeting at a point between Boston and New York the two cars A and B proceed to their respective destinations of New York and Boston. Car A reaches New York 40 minutes after the two cars have met and Car B reaches Boston 90 minutes after they have met. How long did Car A take to cover the distance between Boston and New York?

A. 1 hour

B. 1 hour 10 minutes

C. 2 hours 30 minutes

D. 1 hour 40 minutes

E. 2 hours 10 minutes

We can plug in the answers, which represent the time for A to travel the entire distance.

We should start with the median amount of time, 1 hour + 40 minutes.

Answer choice D: Total time for A = 100 minutes.
Since A travels for 40 minutes after A and B meet, time for A and B to meet = 100-40 = 60 minutes.
Since B travels for 90 minutes after A and B meet, total time for B = 60+90 = 150 minutes.
Let distance = 300 miles.
Rate for A = d/t = 300/100 = 3 miles per minute.
Rate for B = d/t = 300/150 = 2 miles per minute.
When elements work together to cover a distance, we add their rates.
Combined rate for A and B = 3+2 = 5 miles per minute.
Time for A and B to meet = d/r = 300/5 = 60 minutes. Success!

The correct answer is D.

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GmatKiss: Legendary Member; Posts: 2789; Joined: Tue Jul 26, 2011 12:19 amFollowed by: 43 members; Location: Chennai, India; Thanked: 206 times; GMAT Score:640

by GmatKiss » Sat May 19, 2012 11:24 am

GMATGuruNY wrote:
finance wrote:Two cars A and B start from Boston and New York respectively simultaneously and travel towards each other at constant speeds along the same route. After meeting at a point between Boston and New York the two cars A and B proceed to their respective destinations of New York and Boston. Car A reaches New York 40 minutes after the two cars have met and Car B reaches Boston 90 minutes after they have met. How long did Car A take to cover the distance between Boston and New York?

A. 1 hour

B. 1 hour 10 minutes

C. 2 hours 30 minutes

D. 1 hour 40 minutes

E. 2 hours 10 minutes
We can plug in the answers, which represent the time for A to travel the entire distance.

We should start with the median amount of time, 1 hour + 40 minutes.

Answer choice D: Total time for A = 100 minutes.
Since A travels for 40 minutes after A and B meet, time for A and B to meet = 100-40 = 60 minutes.
Since B travels for 90 minutes after A and B meet, total time for B = 60+90 = 150 minutes.
Let distance = 300 miles.
Rate for A = d/t = 300/100 = 3 miles per minute.
Rate for B = d/t = 300/150 = 2 miles per minute.
When elements work together to cover a distance, we add their rates.
Combined rate for A and B = 3+2 = 5 miles per minute.
Time for A and B to meet = d/r = 300/5 = 60 minutes. Success!

The correct answer is D.

Hi,

How can we assume it to be 300?
Also can someone please explain how the same assumption will not lead us to the result if we choose some other option to deal with in the first place.

TIA,
GK

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BestGMATEliza: Master | Next Rank: 500 Posts; Posts: 103; Joined: Mon Jun 23, 2014 11:31 pmFollowed by: 12 members; Thanked: 25 times; GMAT Score:770

by BestGMATEliza » Wed Jul 09, 2014 10:05 pm

So we have car A headed out from Boston to NY and car B headed out from NY to Boston.
Let's say they meet at point P

Boston-------------------------P----------------------NY
Car A>>>---------------------------------------<<< Car B

Let call the distance between Boston and P D1
and the distance between P and NY D2

so we know that A travels at some speed (Sa) for time t over the distance of D1
Sa*(t)=D1

later Car B travels at its speed (Sb) for 90 minutes over the distance of D1
Sb*(90)=D1

we can combine these equations to get:
Sa*(t)=Sb*90
What we ultimately want to find is t, so we should make it the only variable on its side and we get:
t/90=Sb/Sa

Now, lets look at D2
we know that Car A travels at Speed a (Sa) for 40 minutes to get from P to NY
Sa*(40)=D2

and we know that Car b drives for the first t minutes to get from NY to P
Sb*(t)=D2

putting the two together we get
Sa*(40)=Sb*(t)

we can manipulate this equation so that we know the value for Sb/Sa and can combine it with the pink equation and eliminate both Sb and Sb to find t
Sb/Sa=40/t

by combining the final pink and blue equations we can get:
40/t=t/90

cross multiply and we have t*t=3600
so t=60

notice how answer A is 1 hour, this is to trick the people who are so excited about solving for the variable that they forget what the question is asking. Don't be fooled!! Remember that the question is asking for the total time it took A to get from Boston to NY, this is actually t+40 or 1 hour and 40 minutes (D)

Hope this helps!

Eliza Chute
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