Question: Two friends A and B leave City P and City Q simultaneously and travel towards Q and P at constant speeds. They meet at a point in between the two cities and then proceed to their respective destinations in 54 minutes and 24 minutes respectively. How long did B take to cover the entire journey between City Q and City P?
- 60
- 48
- 32
- 36
- 24
Correct Answer: A
Solution and Explanation:
Approach Solution 1:
The problem statement states that:
Given:
- Two friends A and B leave City P and City Q simultaneously and travel towards Q and P at constant speeds.
- They meet at a point between the two cities
- They then proceed to their respective destinations in 54 minutes and 24 minutes respectively.
Find out:
- The time taken by B take to cover the entire journey between City Q and City P.
Let’s assume that Car A travels at the speed of “a”
Let Car B travels at a speed of “b”.
Let us also assume that they meet after “t” minutes.
Hence, the distance traveled by car A before meeting car B = a * t.
Likewise, the distance traveled by car B before meeting car A = b * t.
Therefore, we get,
Distance traveled by car A after meeting car B = a * 54.
Distance traveled by car B after meeting car A = 24 * b.
We also know that,
Since both cars are travelling, the distance traveled by car A after crossing car B = distance traveled by car B before crossing car A (and vice versa).
=> at = 54b ---------- (1)
and bt = 24a -------- (2)
Multiplying equations 1 and 2
we have:
ab * t2 = 54 * 24 * ab
=> t2 = 54 * 24
=> t = 36
Therefore, both cars would have traveled 36 minutes prior to crossing each other.
Or, we can say B would have taken 36 + 24 = 60 minutes to travel the whole distance.
Therefore, the time taken by B take to cover the entire journey between City Q and City P = 60 minutes.
Approach Solution 2:
The problem statement states that:
Given:
- Two friends A and B leave City P and City Q simultaneously and travel towards Q and P at constant speeds.
- They meet at a point between the two cities
- They then proceed to their respective destinations in 54 minutes and 24 minutes respectively.
Find out:
- The time taken by B take to cover the entire journey between City Q and City P.
As per the condition of the question we can infer that;
P ———————Meet———————Q
A leaves P——->. <————-B leaves Q
Let’s consider the speed of A = A
Let’s consider the speed of B = B
(1st)
From point P to Meet= (Speed of A) * (Time it takes to Meet) = AT
From point Q to Meet= (Speed of B) * (Time it takes to Meet) = BT
Therefore, we get:
AT = Meet to P
BT = Meet to Q
(2nd)
Then A takes 54 minutes or 9/10 of an hour to go from Meet to Q
(9/10)A = Meet to Q
And B takes 24 minutes or 2/5 of an hour to go from Meet to P
(2/5)B = Meet to P
If we set up a proportion:
Let the proportion be = Meet to P / Meet to Q
= AT / BT
= (2B/5) / (9A/10)
Now, we need to cancel T and cross-multiply A and B
(A)^2 / (B)^2 = (2/5) / (9/10) = 20 / 45 = 4/9
Let us now take the square root of both sides (A and an are positive values since they are speeds)
A/B = 2/3
Ratio of Speeds= A : B = 2 : 3
Over the same distance, the Ratio of Times taken will be inversely proportional:
Ratio of Times= a : b = 3x : 2x
A takes a Time of = a = 54 minutes to travel from the Meet Point to Point Q
3x= 54 ——-> x = 18
Thus B will take= 2x = 2(18) = 36 minutes to travel from Point Q to Meet Point
Then it takes B another 24 minutes to get to Point P
Total Time for B = 36 + 24 = 60 minutes or 1 hour
Therefore, the time taken by B take to cover the entire journey between City Q and City P = 60 minutes.
“Two friends A and B leave City P and City Q simultaneously and travel towards Q and P at constant speeds”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This topic has been taken from the book “501 GMAT Questions”. The candidates can practice these types of GMAT Problem Solving questions to improve their skills in arithmetic, algebra and geometry. It tests candidates’ skills and efficiency in calculating quantitative problems. The GMAT Quant practice papers further help the candidates to become familiar with different sorts of questions. This enables the candidates to perform better in the GMAT exam.
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