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

Question

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 A at 4p.m. What was the speed of B?

(1) The velocity of Cyclist A was 20 mph.
(2) When Cyclist B overtook cyclist A, both had traveled 80 miles.

(1) The velocity of Cyclist A was 20 mph.
(2) When Cyclist B overtook cyclist A, both had traveled 80 miles.

Archit3110 · Answer

#1
distance travelled by A ; 
20*4 ; 80 miles
so speed of B ; 80/2 ; 40 mph
sufficient
#2
sufficient
IMO D

GMATWhizTeam · Answer

Solution 
 Step 1: Analyse Question Stem 
 • Both started from the same point X.
• Cyclist A travels for 4 hours and cyclist B for 2 hours
• When B overtook A distance covered by both of them is equal.
• Let a and b be the speed of A and B respectively.
 o  4*a = 2*b 
o  b = 2*a   
We need to find the speed of B.
 Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE 
 Statement 1:  The velocity of Cyclist A was 20 mph
 •  a = 20  mph
 o  b=2*a=2*20  
• We can find the speed of B with this information. 
Hence, statement 1 is sufficient, we can eliminate B, C, and E.
 Statement 2:  When cyclist B overtook A, both at traveled 80 miles.
 •  2*b = 80  mph
 b = \frac{80}{2} 
• We can find the speed of B with this information. 
Hence, statement 2 is also sufficient, the correct answer is  Option D .

CrackverbalGMAT · Answer

This is a question on the concept of Relative Speed. Relative speed is the effective speed when two objects are moving simultaneously.

If the two objects are moving in the same direction, the relative speed is the difference of the speeds. 
If the two objects are moving in the opposite direction, the relative speed is the sum of the speeds .

Remember that Relative Speed needs to be considered only when both the objects are moving simultaneously.

Since cyclist A starts at 12 noon, he would have travelled a total of 4 hours by the time he gets overtaken by cyclist B. 
Let the speed of cyclist A be a miles per hour and let the speed of cyclist B be b miles per hour.

The relative speed between the two persons will be (b-a) miles per hour  (note that B is the faster cyclist and hence the difference will be b-a ).

Between 12 pm and 2 pm, cyclist A travelled alone at HIS speed and hence travelled 2a miles.
At 2 pm, cyclist B is at X and cyclist A is 2a miles away from X. We know that this 2a miles was covered in 2 hours. Therefore, 
2 = 2a / b-a because,

Time taken to meet/overtake = Distance between the objects / Relative Speed

Solving the equation above, we have b-a = 2a / 2 = 2. This means, 
b-a = a or b = 2a. As such, if we have to calculate the speed of B, we need the speed of A.

Statement I alone gives us the speed of cyclist A. Statement I alone is sufficient. 
Answer options B, C and E can be eliminated. Possible answer options at this stage are A or D.

Statement II alone tells us that cyclist A had travelled 80 miles in 4 hours. We can calculate his speed using this data. Statement II alone is sufficient.
Answer option A can be eliminated.  The correct answer option is D .

Breaking down the question statement and framing an equation will help you to understand what exactly you need to look for in the statements. This technique is especially useful when the question statement is lengthy and gives you substantial amount of data.

Hope that helps!

Basshead · Answer

The question stem tells us Cyclist A has been traveling for 4 hours; Cyclist B has been traveling for 2 hours at 4 pm when Cyclist B overtakes Cyclist A. The question asks for the speed of Cyclist B. Lets take a look at the statements:

(1) The velocity of Cyclist A was 20mph.

speed = distance / time

Cyclist A:
20 = distance / 4

We can determine the distance Cyclist A traveled was 80.

Cyclist B:
speed = 80 / 2

We can determine the speed of Cyclist B was 40 mph, as the question states Cyclist B traveled at constant velocity. Sufficient.

(2) When Cyclist B overtook Cyclist A, both had traveled 80 miles.

distance = speed * time

80 = speed * 4
Cyclist A's speed was 20 mph.

80 = speed * 2
Cyclist B's speed was 40 mph.

Statement 2 is sufficient.

Answer is D.

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

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

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