Can you please explain what formula I need to do to solve the following problem:
If 3 laps = 5/8 mile, how many laps needs to be completed to run 3 miles?
Don't look for "formulas" to do these kind of questions, use ratios, one of the most powerful tools of math
3 laps = 5/8 mile
x laps = 3 miles
so
3/x = (5/8)/3
cross-multiply
(5/8)x = 9
x = 9(8/5)
=14.4 laps
To solve this problem, you can use ratios.
First, you know that 3 laps is equal to 5/8 mile.
To find out how many laps are needed to run 3 miles, you need to set up a proportion.
Let x represent the number of laps needed to run 3 miles.
You can set up the proportion as follows:
3 laps / x laps = 5/8 mile / 3 miles
To solve for x, you cross-multiply:
3 miles * 5/8 mile = x laps * 1
15/8 miles = x laps
To isolate x, you multiply both sides by the reciprocal of 15/8:
8/15 * 15/8 miles = x laps * 8/15
1 mile = x laps * 8/15
Now, divide both sides by 8/15 to solve for x:
1 mile / (8/15) = x laps
Multiply 1 mile by the reciprocal of 8/15:
1 mile * 15/8 = x laps * (15/8)
15/8 miles = x laps
Therefore, x is equal to 15/8 laps, which is equivalent to 1.875 laps.
So, you would need to complete approximately 1.875 laps to run 3 miles.
To solve the problem, we can use a ratio to find the number of laps needed to run 3 miles.
First, we are given that 3 laps is equal to 5/8 mile.
Next, we want to find the number of laps needed to run 3 miles, which we'll call x laps.
We can set up a proportion using the ratios of laps to distance:
3 laps / (5/8) mile = x laps / 3 miles
To solve the proportion, we cross-multiply:
(5/8)x = 9
To isolate x, we divide both sides of the equation by 5/8:
x = 9 / (5/8)
To divide by a fraction, we can multiply by its reciprocal. The reciprocal of 5/8 is 8/5, so we multiply both sides of the equation by 8/5:
x = 9 * (8/5)
Multiplying the numerators and denominators gives us:
x = 72/5
Therefore, the number of laps needed to run 3 miles is 72/5 laps, which simplifies to 14.4 laps.