SOLUTION: A motorcycle drive travels 15 kph faster than a bicycle rider . The motorcycle drive covers 60 km in two hours than that time it takes the bicycle rider to travel the same distance

                A motorcycle driver travels 15 kph faster than a bicycle rider. 
                The motorcycle driver takes 2 hours less to cover 60 km than it takes the bicycle rider 
                to travel the same distance. What is the mathematical sentence

Let x be the bicycle average rate, in km/h.


Then the motorcycle average rate is (x+15) km/h, according to the condition.


The bicycle takes  hours to cover the same distance.


The difference of times is 2 hours, as the condition states:


     -  = 2   hours.


It is so called "time equation" -- the BASIC equation for such type of problems.


It is the equation -- "the mathematical sentence" -- you asked for.


To solve it, multiply both sides by x*(x+15). You will get


    60*(x+15) - 60x = 2x*(x+15).


Simplify and solve for x


     900 = 2x^2 + 30x

     2x^2 + 30x - 900 = 0

     x^2  + 15x - 450 = 0

     (x+30)*(x-15) = 0.


The roots are -30 and 15, but only positive x= 15 makes sense.


So, you get the ANSWER:  the bicycle average rate is 15 km/h;  the motorcycle average rate is 15+15 = 30 km/h.


CHECK.   = 4 hour for the bicycle and   = 2 hours for the motorcycle with the difference 4-2 = 2 hours.   ! Correct !