If Cathy walks for 2 h and rides her bicycle for 1 h, she can travel 36 km. If she walks for 2 h and rides her bicycle for 2 h, she can travel 56 km. How fast can she walk? How fast can she ride her bike? Let w represent walking and b represent biking.
2w + b = 36
2w + 2b = 56
well, since she walks 2 hours in each case, it is clear that the extra hour of biking gave her an extra 20 km.
b = 20
so, since 2w+20=36, w=8
Thank you so much. I got really confused on the system of equations but I think I understand it now. Thank you :)
Glad to help. Translating words into symbols can be tricky, but the key is just to examine the data carefully. Believe it or not, it gets easier with practice, just like everything else.
To find out how fast Cathy can walk and ride her bicycle, we can set up a system of equations.
Let's assume that Cathy's walking speed is represented by 'w' (in km/h) and her biking speed is represented by 'b' (in km/h).
From the given information, we can create two equations:
Equation 1: Cathy walks for 2 hours and rides her bicycle for 1 hour, traveling a total distance of 36 km.
2w + 1b = 36
Equation 2: Cathy walks for 2 hours and rides her bicycle for 2 hours, traveling a total distance of 56 km.
2w + 2b = 56
Now, we can solve this system of equations to find the values of 'w' and 'b'.
First, let's multiply Equation 1 by 2 to eliminate the variable 'b':
(2w + 1b) * 2 = 36 * 2
4w + 2b = 72
Next, we'll subtract Equation 2 from the adjusted Equation 1 to eliminate the variable 'w':
(4w + 2b) - (2w + 2b) = 72 - 56
2w = 16
w = 8
Now that we know the value of 'w', we can substitute it into either Equation 1 or Equation 2 to find 'b'.
Using Equation 1:
2w + 1b = 36
2(8) + b = 36
16 + b = 36
b = 20
Therefore, Cathy can walk at a speed of 8 km/h and ride her bicycle at a speed of 20 km/h.