A woman can bicycle 66 miles in the same time as it takes her to walk 24 miles. She can ride 7 mph faster than she can walk. How fast can she walk?
Using r as your variable to represent the rate at which she walks, write an equation using the information as it is given above that can be used to solve this problem.
Well, well, well, looks like we've got a math problem here! Let's break it down, shall we?
So, if we let r be the rate at which she walks, we know she can bicycle 7 mph faster than she walks. That means the rate at which she bikes would be r + 7.
Now, the problem tells us that she can bicycle 66 miles in the same time it takes her to walk 24 miles. But we know that time = distance / rate. So, for walking, the time would be 24 / r, and for biking, the time would be 66 / (r + 7).
So our equation would be:
24 / r = 66 / (r + 7)
Now, let's put our math hats on and solve this equation!
Let's break down the information given in the problem:
1. A woman can bicycle 66 miles in the same time as it takes her to walk 24 miles.
2. She can ride 7 mph faster than she can walk.
Using this information, we can set up the following equation:
Time taken to walk 24 miles = Time taken to bicycle 66 miles
Distance / Rate = Time
The time taken to walk 24 miles can be calculated as 24 / r, where r is the rate at which she walks.
The time taken to bicycle 66 miles can be calculated as 66 / (r + 7), as she can ride 7 mph faster than she can walk.
Therefore, the equation that represents the information given is:
24 / r = 66 / (r + 7)
To solve this problem, let's use the formula:
Time = Distance / Rate
Given that the woman can bicycle 66 miles in the same time it takes her to walk 24 miles, we can write two equations:
For walking:
Time (walk) = 24 miles / Rate (walk)
For bicycling:
Time (bike) = 66 miles / Rate (bike)
We know that the woman rides 7 mph faster than she walks, so we can express the rate of bicycling as Rate (bike) = Rate (walk) + 7 mph.
Therefore, the equation can be written as:
24 / (Rate (walk)) = 66 / (Rate (walk) + 7)
Now we have an equation that relates the rates of walking and bicycling.
Since time = distance/speed,
66/(r+7) = 24/r