So for this we will be writing two equations: one representing rachel and the other with oliver. I'll be using the slope-intercept form, which is y = mx + b (m = slope, b = y-intercept). The slope is considered the constant rate of the equation, which in this case its "3 bracelets an hour" and "2 bracelets an hour". The y-intercept is considered the initial value, which in this case with Oliver "he already has 5 bracelets." Using the info above, these are our 2 equations:
Let x = # of hours and y = total bracelets
With these equations, thanks to the transitive property (if a = b and a = c then b = c) she can set 3x and 2x + 5 equal to each other and solve for the number of hours it would take for them to have the same amount of bracelets.