+0  
 
0
44
1
avatar

Two men, A and B, start at the same point, walk in opposite directions, and reach their respective destinations, X and Y, each in one hour.  Had they exchanged destinations from the start, A would have arrived at Y 35 minutes after B would have arrived at X.  Find the ratio of A's speed to B's speed.

 Dec 8, 2019
 #1
avatar+106519 
+1

A  must walk  at a rate of   X mph

B must   walk at  at a rate of   Y mph

 

And when they switch destinations

 

Y / X    =  X  / Y  +    35/60

 

Y / X    =  X /Y   +  7/12

 

Y/X   - X/Y  =  7/12

 

Y^2   - X^2               7

_________   =       ____

       XY                    12

 

12 (Y^2 - X^2)  =  7XY

 

12Y^2  - 12X^2  =  7XY

 

12Y^2 - 7XY  - 12X^2   =  0

 

(4Y + 3X) (3Y - 4X)  =  0

 

Only the  second  factor gives us what we want

 

3Y   -  4x  =  0

 

4X  = 3Y

 

X  =  (3/4)Y

 

X/Y  = 3/4

 

So.....the ratio of A's speed to B's speed must be  X : Y    =         3  :  4

 

 

cool cool cool

 Dec 9, 2019

15 Online Users

avatar