Question

Two cyclists start at the same point and travel in opposite directions. One cyclist travels

Answer 1

Distance = rate times time.

Let the first cyclist's rate be r1 and the 2nd cyclist's rate be r2.

Let r2 = r1 + 10   (km per hour).

The total distance between them after 3 hours is 174 km; using the distance= rate times time formula, we also get:

r1(3 hrs) + r2(3 hrs) = 174 km
Then
r1(3 hrs) + (r1+10)(3hrs) = 174 km

Then 3r1 + 3r1 + 30 = 174 

6r1 = 144, and r1 = 24 km/hr.  Then r2 = (24 + 10) km/hr = 34 km/hr.