Find the rate of speed.

Question

A cyclist began a 513 mile ride across a state at the western edge of the state.  At the same time a car traveling toward it leaves the eastern side of the state.  If the cyclist and car met after 9.5 hours and the car traveled 37.8 mph faster than the cyclist, what is the average rate of each.

Answer 1

Sonna, if the cyclist travelled c mph, then the car travelled c + 37.8 mph, right?

 

How do we find distance? Rate x time. Together, the two travelled 513 miles.

 

9.5(c) + 9.5(c + 37.8) = 513

 

I bet you can finish!

Answer 2

Ok, The total miles traveled was 513, the average rate of the car is 37.8 mph faster than that of the cyclist.

 

             Car rate = Cyclist rate +37.8 mph

 

The total miles were traveled by a combination of the cyclists time traveled at an average rate plus the cars time traveled at an average rate. 

 

              Cyclist rate(9.5 hrs)+Car rate(9.5 hrs)=513 miles

       

Substitute the car rate and distribute out the time

 

               9.5 hrs(Cyclist rate + (Cyclist rate + 37.8 mph)) = 513 miles

 

Solve for the cyclist rate and use it to solve for the car rate,

 

               2 Cyclist rate +37.8 mph= 513 mile/9.5 hrs

               2 Cyclist rate = 54 mph - 37.8 mph

               Cyclist rate = 16.2 mph /2

               Cyclist rate = 8.1 mph

 

 

               Car rate = 8.1 mph + 37.8 mph

               Car rate = 45.9 mph