Two bicyclists started biking toward each other when they were 88 miles apart. three hours later there were 4 miles left between them. how fast was each bicyclist going if one of them was 4 mph slower than the other?

Alright, lets get started.

Suppose first bicyclist speed is = x mph

As given in question, second one is 4 mph slower than first, hence

Speed of second bicyclist is = (x-4) mph

They both travels 3 hrs so,

distance covered by first bicyclist :

distance covered by second bicyclist :

4 miles were still left after 3 hrs of driving.

It means they covered 88 - 4 = 84 miles together

Adding 12 in both sides

Dividing 6 in both sides

Means speed of first bicyclist = 16 mph

Speed of second bicyclist = mph

Hence speed of both bicyclist are 16 mph and 12 mph. : Answer

Hope it will help :)

The general form for a hyperbola with the center at the origin and a vertical transverse axis is:
y2/a2 - x2/b2 = 1

From the given:
a = 12

To get b, we use the given distance between the foci.Since it's 26,
c = 26/2 = 13

Using this defintion:
c2 = a2 + b2
b = sqrt(c2 - a2) = sqrt (13^2 - 12^2) = 5

The equation therefore is:
y2/13^2 - x2/5^2 = 1
or
y2/169 - x2/25 = 1