math help

Question

1.
A bicyclist travels at a constant rate on her bicycle. Biking with the wind, it takes 2.6 hours to travel 52 miles. Biking
against the
wind, the return trip takes 4 hours. If there was no wind, how fast was the cyclist
biking?

Answer 1

d=rt

52=(r+w)2.6

52=(r-w)4

20=r+w

13=r-w

add the equations

33=2r

r=33/2

r=16.5 mph was the speed of the cyclist without the wind

Answer 2

Hi Jake,

 

The solution to this problem requires understanding how the wind changes the overall rate of the bicyclist.

 

What can be said about the cyclist's overall rate when the cyclist is traveling with the wind? Does this rate represent how fast the cyclist is biking? Does the wind increase or decrease the overall rate of motion?

 

Similarly, what can be said about the cyclist's overall rate when the cyclist is traveling against the wind? Does this rate represent how fast the cyclist is biking? Does the wind increase or decrease the overall rate of motion?

 

Each of the parts above can be summarized into algebraic equations that tell us how fast the cyclist is biking and how fast the wind is blowing.

 

Since we know the time and distance involved in each part, what can we calculate from those times and distances? Do these numbers represent the rate at which the cyclist is biking or do they represent the overall rate of motion?

 

Using these calculations with the algebraic equations, it is possible to calculate how fast the cyclist is biking. Although the question asks for the cyclist's speed in the absence of wind, this is just another way of asking how fast the cyclist is biking.