366 Mr. BappaceE on the Influence of Signs 
and by reduction 
gos CSBch cdh 
eg +df ° 
This same question with the following data may be solved 
in nearly the same way, 
v = velocity per second of 4, 
s = the space one (A) is distant from the other B, 
t = the time mm seconds one (B) starts before the other. 
Since the velocities are both positive, the bodies move in the 
same direction, and x being the distance of the point where they 
meet from the place of 4, the number of seconds which 4 will 
take to pass over it, will be found from the ratio 
SY Py eS 
v’ 
the distance of the other body from the same point will be 
x —s, and the time it takes to arrive will be <>}, but the other 
body began to move ¢ seconds before B, therefore ¢ added to the 
5 : . rT—s 
time of its motion must equal Saree 
x 2s 
~+t=—--—-: 
vD ie) o 
hence 
s fe vit 
t+—=a([--~), 
° v v Vv 
and 
s 
ees t ; 
a ag s + tv 
He oe o—v 
vy ov 
If A move in an opposite direction, its velocity must be accounted 
negative; hence in that case v' becomes — v’, and 
