Answer:the woman can walk at a speed of 3.5 miles per hour
Explanation:
Let's denote the speed at which the woman can walk as "W" (in miles per hour) and the speed at which she can ride her bicycle as "B" (in miles per hour).
We are given two pieces of information:
The woman can bicycle 27 miles in the same time it takes her to walk 7 miles.
She can ride 10 mph faster than she can walk.
From the first piece of information, we can set up an equation based on the time it takes for both activities. Time = Distance / Speed.
For walking: Time(W) = 7 / W
For bicycling: Time(B) = 27 / B
Since the time for both activities is the same, we can equate them:
7 / W = 27 / B
Now, let's use the second piece of information: "She can ride 10 mph faster than she can walk." This can be expressed as:
B = W + 10
Now we have a system of two equations:
7 / W = 27 / B
B = W + 10
We can solve this system to find the speed at which she can walk (W).
First, we'll use equation (2) to express B in terms of W:
B = W + 10
Now, substitute this expression for B into equation (1):
7 / W = 27 / (W + 10)
To solve for W, cross-multiply:
7(W + 10) = 27W
Expand and simplify:
7W + 70 = 27W
Now, subtract 7W from both sides:
70 = 20W
Now, divide by 20 to solve for W:
W = 70 / 20
W = 3.5
So, the woman can walk at a speed of 3.5 miles per hour.