Math problem involving distance rate and time

Question

a bicyclist travels at a constant rate on her bicycle. biking with the wind, it takes 3.4 hours to travel 68 miles. biking against the wind, the return trip takes 5 hours. if there was no wind, how fast was the cyclist biking?

Answer 1

Let x = speed of bike if there is no wind

      y = speed of wind

 

speed with the wind  = x + y

speed against the wind = x - y

 

Distance = (Rate)(Time)

 

Distance with the wind = 68 = 3.4(x + y)

Distance against the wind = 68 = 5(x - y)

 

So, x + y = 20

      x - y = 13.6

 

Adding the equations, we get 2x = 33.6

 

                                                     x = 16.8 mph