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Alice and Bob traveled in the same direction along the same route at t
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MathRevolution
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Alice and Bob traveled in the same direction along the same route at t [#permalink] New post  21 Mar 2018, 01:52
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[GMAT math practice question]

Alice and Bob traveled in the same direction along the same route at their respective constant speeds of 12 km per hour and 6 km per hour. They each started to travel from their own houses. Bob’s house is halfway between Alice’s house and the destination. After passing Bob, Alice took 10 minutes to reach the destination. How many minutes did it take Bob to reach the destination after Alice passed him?

A. 5 min
B. 6 min
C. 8 min
D. 10 min
E. 20 min
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Alice and Bob traveled in the same direction along the same route at t [#permalink] New post  21 Mar 2018, 02:12
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MathRevolution wrote:
[GMAT math practice question]

Alice and Bob traveled in the same direction along the same route at their respective constant speeds of 12 km per hour and 6 km per hour. They each started to travel from their own houses. Bob’s house is halfway between Alice’s house and the destination. After passing Bob, Alice took 10 minutes to reach the destination. How many minutes did it take Bob to reach the destination after Alice passed him?

A. 5 min
B. 6 min
C. 8 min
D. 10 min
E. 20 min


Since the speed of Alice is double the speed of bob, the time taken by alice is half the time taken by Bob

Alice takes 10 mins thus bob takes \(\frac{10}{1/2}\) = 10 x2 = 20

(E)
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Alice and Bob traveled in the same direction along the same route at t [#permalink] New post  21 Mar 2018, 09:38
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MathRevolution wrote:
[GMAT math practice question]

Alice and Bob traveled in the same direction along the same route at their respective constant speeds of 12 km per hour and 6 km per hour. They each started to travel from their own houses. Bob’s house is halfway between Alice’s house and the destination. After passing Bob, Alice took 10 minutes to reach the destination. How many minutes did it take Bob to reach the destination after Alice passed him?

A. 5 min
B. 6 min
C. 8 min
D. 10 min
E. 20 min

Convert rates to minutes.
A's rate in minutes:
\(\frac{12km}{1hr}=\frac{12km}{60mins}=\frac{1km}{5mins}\)

B's rate in minutes:
\(\frac{6km}{1hr}=\frac{6km}{60mins}=\frac{1km}{10mins}\)

Information to ignore or avoid:
1) Bob's house as a halfway point
2) Relative speed
3) Whatever happens before the passing point

As soon as Alice passes Bob, the chase is over. Both travel the same distance to the end.*

We need only two pieces of information:

1) the distance from pass point to end, which we can derive from Alice's time; and

2) the time it takes for Bob to travel that distance, which we can derive from his rate

Distance to end
In 10 minutes, the distance Alice covers is
\(D= R*T\), so
\(D= \frac{1km}{5mins}* 10mins = 2\) kms

Time Bob takes to cover distance of 2km
\(R*T= D\), so \(T =\frac{D}{R}\)

\(T =\frac{2km}{\frac{1km}{10mins}}=(2km*\frac{10mins}{1km})= 20\) minutes

Answer E

* Distance from pass point to end is same for both
Point at which A passes B
House B--->---B|------------|
House B---->--A|------------|

A is in front of B
House B--->--->|B->---------|
House B---->-->|-----A-->---|
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Re: Alice and Bob traveled in the same direction along the same route at t [#permalink] New post  22 Mar 2018, 23:22
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=>

After Alice passed Bob, she traveled for \(10\) more minutes.
Since Bob’s speed is half of Alice’s speed, he took a further \(20\) minutes to reach the destination.

Therefore, the answer is E.

Answer: E
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Re: Alice and Bob traveled in the same direction along the same route at t [#permalink] New post  24 Mar 2018, 18:42
If bob house is halway between alice and destination and if slice speed is twice that of bob

How are they supposed to cross each other they will meet directly at destination

alice has to cover 2d distance with 12km/hr implies time taken is 2d/12=d/6

bob jas to travel d with speed 6km/hr hence time taken is d/6

so they meeet directly in destination


please explain
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Alice and Bob traveled in the same direction along the same route at t [#permalink] New post  24 Mar 2018, 21:06
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sameeruce08 wrote:
If bob house is halway between alice and destination and if slice speed is twice that of bob

How are they supposed to cross each other they will meet directly at destination

alice has to cover 2d distance with 12km/hr implies time taken is 2d/12=d/6

bob jas to travel d with speed 6km/hr hence time taken is d/6

so they meeet directly in destination

please explain

sameeruce08 , the "halfway" info is to let us know that Alice starts behind Bob.

As far as distance:
Alice does travel 2d, but we don't care about that because we don't know start times.

After she passes him, both travel same distance.

We find distance from her rate and time. In minutes. (Or fraction of hour.)

Then find Bob's time from distance and rate.

All that matters: separate rates and times.

She travels at 12 km per hour.
One hour = 60 minutes.
Rate: She travels 12 km in 60 minutes:
D= \((\frac{12km}{60mins}*10 minutes) = 2\)kms

Bob's speed = 6 km/hr, OR 6 km in 60 minutes.

Bob's time?
\(T = \frac{D}{R}\)
\(T=\frac{2}{(\frac{6}{60})}=(2*\frac{60}{6})=20\) mins

OR get time from Bob's unit rate = \(\frac{6km}{60mins} =\frac{1km}{10mins}\)

To go 2 km, at a rate of 1 km per 10 minutes, it will take him 2 * 10 = 20 minutes.

Hope that helps.
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Re: Alice and Bob traveled in the same direction along the same route at t [#permalink] New post  25 Jun 2019, 06:13
MathRevolution wrote:
[GMAT math practice question]

Alice and Bob traveled in the same direction along the same route at their respective constant speeds of 12 km per hour and 6 km per hour. They each started to travel from their own houses. Bob’s house is halfway between Alice’s house and the destination. After passing Bob, Alice took 10 minutes to reach the destination. How many minutes did it take Bob to reach the destination after Alice passed him?

A. 5 min
B. 6 min
C. 8 min
D. 10 min
E. 20 min


After crossing Bob, Alice will travel 10(min)x12(km/hr)
And this distance is constant and Bob also will travel the same distance in x(min)x6(km/hr)
equating, x=20min
Answer: E
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Re: Alice and Bob traveled in the same direction along the same route at t [#permalink] New post  23 Oct 2019, 00:25
In order to arrive at the correct answer we need to consider the distance that Alice will cover in 10 minutes after catching up with Bob. At 12km per hour, Alice will cover a distance of 10/60 x 12 = 2km.
Having calculated the distance, we can used this figure to calculate the time that it would take Bob to cover 2km
At a speed of 6km per hour, Bob will cover 2km in 2/6 x 60 = 20 minutes.
Therefore, the correct answer is E.
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Re: Alice and Bob traveled in the same direction along the same route at t [#permalink] New post  28 Oct 2019, 08:53
Are we assuming that they didn't start at the same time and Bob started only when Alice crossed his house?
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Re: Alice and Bob traveled in the same direction along the same route at t [#permalink] New post  28 Oct 2019, 09:13
Nope. They both started at same time. Since Bob's house is halfway between Alice's house and destination..and Alice being 2x(12kmph) faster than bob is... Alice would have crossed bob somewhere between bob's house and destination. Given in the question is the time Alice took AFTER crossing bob and ask is for time taken by bob to reach destination after alice crossed.

Hope it helps!


PinakiRDas wrote:
Are we assuming that they didn't start at the same time and Bob started only when Alice crossed his house?

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Re: Alice and Bob traveled in the same direction along the same route at t [#permalink] New post  31 Mar 2020, 11:42
MathRevolution wrote:
[GMAT math practice question]

Alice and Bob traveled in the same direction along the same route at their respective constant speeds of 12 km per hour and 6 km per hour. They each started to travel from their own houses. Bob’s house is halfway between Alice’s house and the destination. After passing Bob, Alice took 10 minutes to reach the destination. How many minutes did it take Bob to reach the destination after Alice passed him?

A. 5 min
B. 6 min
C. 8 min
D. 10 min
E. 20 min


Given:
1. Alice and Bob traveled in the same direction along the same route at their respective constant speeds of 12 km per hour and 6 km per hour.
2. They each started to travel from their own houses.
3. Bob’s house is halfway between Alice’s house and the destination.
4. After passing Bob, Alice took 10 minutes to reach the destination.

Asked: How many minutes did it take Bob to reach the destination after Alice passed him?

3. Bob’s house is halfway between Alice’s house and the destination.

Alice House -----------------x km -----------------Bob's House ---------------------x km ------------------------Destination

4. After passing Bob, Alice took 10 minutes to reach the destination.
Distance travelled by Alice = (10 /60) * 12 = 2 km
Time taken by Bob to cover 2 km = 2/6 hr = 20 mins

IMO E
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Re: Alice and Bob traveled in the same direction along the same route at t [#permalink]
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