Two friends start walking towards each other with speeds in the ratio

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.

A. 155 meters
B. 160 meters
C. 165 meters
D. 170 meters
E. 175 meters

A. 155 meters
B. 160 meters
C. 165 meters
D. 170 meters
E. 175 meters

Jawad001 · Accepted Answer

Let two friends meet after t

4t -3t =25
 t = 25

Their total initially separated distance = 7t = 7 x 25 = 175(E)

CareerGeek · Answer

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 = \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 = 175   meters

IMO Option E

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Gauravji21 · Answer

Can we use the ratio directly ?..

I mean the speeds are in the ratio 3 : 4.. it is same as 6 : 8. If we take speed ratio as 6:8, then the answer will vary. Normally i will write in the form of a multiple of a constant such as 3x & 4x or 3K & 4K.

Ajinkyagupta88 · Answer

Difference is of 1 parts (4-3) which is given as 25.
Since, speed and distance is directly proportional.

Thus, 7 parts (4+3) will be 7*25=175

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chrtpmdr · Answer

Can I just cancel the 'v' as of rules of algebra or did you have another rationale for canceling the variable 'v'?

Fdambro294 · Answer

Concept: since the2 friends both depart at the same time and travel for the same time up until the meet, Time traveled is CONSTANT for the 2 friends.

When Time is held Constant:

the RATIO of the 2 friends’ Speeds is DIRECTLY Proportional to the RATIO of the Distance the 2 friends can cover in that constant-same travel Time.

Call the 2 friends A and B

Speed of A : Speed of B = 3 : 4 = Distance covered by A : Distance covered by B = D : D + 25

Setting the Ratios Equal you get—-

3 / 4 = D / (D + 25)

Solving for D and D + 25 you get:

D = 75

(D + 25) = 100

Friend A travels 75 to meeting point.

+

Friend B travels 100 to meeting point
__________________________

Total of 175 separated them

-E-

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KANNUPRIYA17 · Answer

Let the distance travelled by the person who travelled less distance be x
Then the distance travelled by the person who walked 25 kms more is- x+25

x+25/x = 4/3
x=75
total distance = x+x+25=175.

Chibvike · Answer

Let the distance covered by the slower friend be x meters, and since the ratio of their speeds is 3:4, the faster friend would have covered a distance of 4/3 meters when they meet 
 We are also told that the faster friend covers 25 meters more than the slower friend, so: 
 4/3 x=x+25

To eliminate the fraction, multiply through by 3: 
 4x=3(x+25) 
 
Now expand the right-hand side: 
 4x=3x+75 
 
Subtract 3x3x from both sides:

x=75 
 
The slower friend covers x=75meters, and the faster friend covers 4/3 ×75=100 meters. 
 
Thus, the total distance that separated them initially is: 
 
75+100=175 meters

Answer choice; E

Two friends start walking towards each other with speeds in the ratio

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Two friends start walking towards each other with speeds in the ratio

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