The question is in details.?
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The question is in details.?

[From: Mathematics] [author: ] [Date: 01-07] [Hit: ]
The question is in details.?Two riders on horseback simultaneously leave Village A. They proceed withdifferent but constant speeds to Village B and then return without stopping.On her way back to Village A, one of the riders overtakes the ot......


The question is in details.?
Two riders on horseback simultaneously leave Village A. They proceed with different but constant speeds to Village B and then return without stopping. On her way back to Village A, one of the riders overtakes the other, meeting her at a point located m miles from Village B. Upon returning to Village A, she leaves...
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answers:
jibz say: Let D be the distance in miles between the two villages. On their first encounter the faster rider has traveled a distance of

D+m

miles while the slower rider has traveled a distance of

D–m

miles. On their second encounter the faster rider has traveled a distance of (2 + 1/3)D i.e.

(7/3)D

miles while the slower rider has traveled a distance of (1 + 2/3)D i.e.

(5/3)D

miles. So the faster rider is (7/3) / (5/3) i.e. 7/5 times more ground than the slower rider. Hence

D+m = (7/5)(D–m).

Solving for D we get D = 6m.
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Ian H say: Use a numerical example to get the idea and convert that to algebra.
Imagine u has speed 3 and v has speed 5 with distance d = 10 miles
After 2 hours v is at B, u is at 6 from A which is 4 from B
After d/v hours v is at B, u is at ud/v from A or (v – u)d/v from B
That gap gets divided in ratio 3 to 5 or u to v
u is at 6 + (3/8)*4 = 7.5 while v is at 10 - (5/8)*4 = 7.5
u is at (u/v)d + [u/(v + u)]*[(v – u)d/v] = 2ud/(v + u) = m
v is at d – [v/(v + u)]* (v – u)d/v = 2ud/(v + u) = m

After 4 hours v is at A while u has gone 10 + 2 miles so he is 8 from A
After 2d/v hours v is at A while u is 2(v – u)d/v from A
That gap of 8 gets divided in ratio 3 to 5 or u to v
v is at (5/8)*8 = 5 from A
u is at 8 - (3/8)*8 = 5 from A
In the created example she meets other at 5/10 or one HALF of the distance between Village A and Village B, whereas your given aim is to meet at a THIRD.
Complete the algebra equivalent and equate it to 1/3 to work out answer.
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Andrew say: It's your homework assignment, kid, not mine. I graduated already and my days of doing homework are over. Enjoy.
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qcmkg say: nfyhksos
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Sean say: .
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