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# Cyclist A leaves point X at 12 noon and travels at constant velocity

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Joined: 02 Sep 2009
Posts: 58445
Cyclist A leaves point X at 12 noon and travels at constant velocity  [#permalink]

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14 Jan 2018, 06:45
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Difficulty:

55% (hard)

Question Stats:

54% (01:31) correct 46% (02:01) wrong based on 99 sessions

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Cyclist A leaves point X at 12 noon and travels at constant velocity in a straight path. Cyclist B leaves point X at 2 p.m. travels the same path at constant velocity, and overtakes cyclist A at 4p.m. At what speed was cyclist B traveling?

(1) Cyclist A traveled 15 miles in the first hour.
(2) The rate of cyclist B is twice that of cyclist A.

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Re: Cyclist A leaves point X at 12 noon and travels at constant velocity  [#permalink]

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14 Jan 2018, 14:28
Bunuel wrote:
Cyclist A leaves point X at 12 noon and travels at constant velocity in a straight path. Cyclist B leaves point X at 2 p.m. travels the same path at constant velocity, and overtakes cyclist A at 4p.m. At what speed was cyclist B traveling?

(1) Cyclist A traveled 15 miles in the first hour.
(2) The rate of cyclist B is twice that of cyclist A.

We know the total time of B so all we need is their total distance.
We'll look for an answer that gives us this information, a Logical approach.

(1) Since A travels at a constant speed then we can multiply 15 by 4 hours to get the distance A cycled which is also the distance B cycled.
Sufficient!

(2) This gives us no information on the distance and is not helpful.
(in fact, it only restates information we already know as B travels the same distance as A in half the time = twice the rate)
Insufficient.

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Re: Cyclist A leaves point X at 12 noon and travels at constant velocity  [#permalink]

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15 Jan 2018, 00:00
Cyclist A leaves point X at 12 noon and travels at constant velocity in a straight path. Cyclist B leaves point X at 2 p.m. travels the same path at constant velocity, and overtakes cyclist A at 4p.m. At what speed was cyclist B traveling?

(1) Cyclist A traveled 15 miles in the first hour.
(2) The rate of cyclist B is twice that of cyclist A.

Hi,

Distance covered by B in 2 hrs = distance covered by A in 4 hrs.
Therefore 2B=4A
OR B=2A where A and B are the speed of A and B

1.A=15 hence b=30;
sufficient;
2. repeats the given premise. insufficient.
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Joined: 26 Mar 2013
Posts: 2344
Cyclist A leaves point X at 12 noon and travels at constant velocity  [#permalink]

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15 Jan 2018, 05:34
DavidTutorexamPAL wrote:
Bunuel wrote:
Cyclist A leaves point X at 12 noon and travels at constant velocity in a straight path. Cyclist B leaves point X at 2 p.m. travels the same path at constant velocity, and overtakes cyclist A at 4p.m. At what speed was cyclist B traveling?

(1) Cyclist A traveled 15 miles in the first hour.
(2) The rate of cyclist B is twice that of cyclist A.

We know the total time of B so all we need is their total distance.
We'll look for an answer that gives us this information, a Logical approach.

(1) Since A travels at a constant speed then we can multiply 15 by 4 hours to get the distance A cycled which is also the distance B cycled.
Sufficient!

(2) This gives us no information on the distance and is not helpful.
(in fact, it only restates information we already know as B travels the same distance as A in half the time = twice the rate)
Insufficient.

Hi David,

In statement 1, Could the speed second and third hour be different than the speed in first hour? does not it affect the calculation?

Suppose this example 1:

speed of 1st hr = 15,
speed of 2nd hr = 20
speed of 3rd hr = 10
speed of 4th hr = 5

Total distance = 50

Suppose this example 2:

speed of 1st hr = 15,
speed of 2nd hr = 25
speed of 3rd hr = 15
speed of 4th hr = 25

Total distance = 80

So we in the same 4 hours there would different speeds leading to different values of distance.

Where did I go wrong?
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Joined: 07 Dec 2017
Posts: 1153
Re: Cyclist A leaves point X at 12 noon and travels at constant velocity  [#permalink]

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15 Jan 2018, 05:50
1
Mo2men wrote:
DavidTutorexamPAL wrote:
Bunuel wrote:
Cyclist A leaves point X at 12 noon and travels at constant velocity in a straight path. Cyclist B leaves point X at 2 p.m. travels the same path at constant velocity, and overtakes cyclist A at 4p.m. At what speed was cyclist B traveling?

(1) Cyclist A traveled 15 miles in the first hour.
(2) The rate of cyclist B is twice that of cyclist A.

We know the total time of B so all we need is their total distance.
We'll look for an answer that gives us this information, a Logical approach.

(1) Since A travels at a constant speed then we can multiply 15 by 4 hours to get the distance A cycled which is also the distance B cycled.
Sufficient!

(2) This gives us no information on the distance and is not helpful.
(in fact, it only restates information we already know as B travels the same distance as A in half the time = twice the rate)
Insufficient.

Hi David,

In statement 1, Could the speed second and third hour be different than the speed in first hour? does not it affect the calculation?

Suppose this example 1:

speed of 1st hr = 15,
speed of 2nd hr = 20
speed of 3rd hr = 10
speed of 4th hr = 5

Total distance = 50

Suppose this example 2:

speed of 1st hr = 15,
speed of 2nd hr = 25
speed of 3rd hr = 15
speed of 4th hr = 25

Total distance = 80

So we in the same 4 hours there would different speeds leading to different values of distance.

Where did I go wrong?

Hi Mo2men,

The question states "at constant velocity" for both cyclists.
So the speed is the same during all the hours... otherwise you would be correct!
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Posts: 2344
Re: Cyclist A leaves point X at 12 noon and travels at constant velocity  [#permalink]

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15 Jan 2018, 05:53
1
DavidTutorexamPAL wrote:

Hi Mo2men,

The question states "at constant velocity" for both cyclists.
So the speed is the same during all the hours... otherwise you would be correct!

Good point

Re: Cyclist A leaves point X at 12 noon and travels at constant velocity   [#permalink] 15 Jan 2018, 05:53
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