Question: Two friends start walking towards each other with speeds in the ratio 3 : 4. When they meet it is found that the faster of them has covered 25 meters more than the slower. Find the distance that separated them initially if they are walking in opposite directions, but obviously towards each other.
- 155 meters
- 160 meters
- 165 meters
- 170 meters
- 175 meters
“Two friends start walking towards each other with speeds in the ratio 3 : 4.”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “The Official Guide for GMAT Reviews”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.
Solution and Explanation:
Approach Solution 1:
This above given question is a time and distance problem. Let us consider the distance traveled by the first friends be d. The distance traveled by the second friend is d+25. So, the relative speed for both the friends can be considered as 3v and 4v.
So, the time taken to travel and meet each other is the same. Then the equation becomes
t=\(\frac{d}{3v}\) and t=\(\frac{d+25}{4v}\)
implies that \(\frac{d}{3v}\)=\(\frac{d+25}{4v}\)
equating both the sides,
4d=3(d+25)
implies that 4d=3d+75
So the value of d=75
Hence, the total distance traveled by them initially =d+d+25=175 meters,
Correct Answer: E
Approach Solution 2:
It is given in the above question that two friends both depart at the same time. They travel for the same time up until they meet. So the time traveled remains constant for both friends.
When time is held constant, the ratio of speed is directly proportional to the ration of distance traveled by them. Let the first friend be A and the second be B.
So, speed of A : Speed of B = 3 : 4
Therefore, Distance covered by A : Distance covered by B = D : D + 25
equating both the sides,
\(\frac{3}{4}\)= \(\frac{D}{D+25} \)
Solving for D and D + 25 we get:
D = 75
Implies that (D + 25) = 100
Therefore, Friend A travels 75 to meeting point + Friend B travels 100 to meeting point = Total of 175 separated them.
Correct Answer: E
Approach Solution 3:
Let the distances traveled by them be ‘d’ & ‘d + 25’ meters and respective speeds be 3v & 4v
Time taken by each of them to meet each other is same.
—> t=d\(\frac{d}{3v}\) & t=\(\frac{d+25}{4v}\)
—> \(\frac{d}{3v}\)=\(\frac{d+25}{4v}\)
—> 4d=3(d+25)
—> 4d=3d+75
—> d=75
Total distance between them initially = d+d+25=2∗75+25=175d+d+25=2∗75+25=175 meters
Correct Answer: E
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