need to solve a word problem using linear equation in slope form.
Ben walks 3 miles per hour, and runs at 6 miles per hour. Runs and walks a total of distance of 210 miles per week.
Is this correct
210 = 3/6m +b - equation to show relation of hours run to walk
B. is Ben runs for 25, how many does he walk
210 = 6(25) +3(x)
nope. distance = speed * time
If the walk/run times are w and r, then
3w + 6r = 210
r = 35 - 1/2 w
w = 70 - 2r
you say Ben runs for 25. 25 what? hours, minutes, miles?
If miles, then the run time is 25/6 hrs.
Use that to find the w value
Your equation hints that he ran for 25 hours. I think you will find that it will be hard to come up with a reasonable value for x.
I meant 25 minutes
here is the 2nd part of the question
B. Ben runs for 25 hours. For how many hours does he walk?
To solve the word problem using linear equations in slope form, we need to define our variables. Let's use the following:
m = number of hours Ben walks
b = total distance Ben walks in miles
Now let's set up the equation to represent the relationship between the hours Ben runs and walks:
Total distance = Distance walked + Distance run
The distance walked can be calculated using the formula: Distance = Speed * Time.
Given that Ben walks at 3 miles per hour and runs at 6 miles per hour, we can write the equation as:
210 = 3m + 6(25)
Here, 6(25) represents the distance Ben runs in 25 hours since we know his running speed. We can solve this equation to find the value of m, which will give us the number of hours Ben walks.
Let's continue by simplifying the equation:
210 = 3m + 150
To isolate the variable term, we can subtract 150 from both sides:
210 - 150 = 3m
60 = 3m
Now, divide both sides by 3 to solve for m:
m = 60/3
m = 20
Therefore, Ben walks for 20 hours in a week if he runs for 25 hours.