Tiffany can run 12 miles in the same time it takes her to bicycle 72 miles. If her bicycling rate is 20mi/hr faster than her running rate, find each rate.
Let X = running rate, so X +20 = cycling rate.
Since rate = miles/time, then time = miles/rate. Since the time for both is the same:
12/X = 72/(X + 20)
You should be able to take it from here.
I hope this helps. Thanks for asking.
To solve the equation 12/X = 72/(X + 20), we can cross multiply:
12(X + 20) = 72X
Now distribute:
12X + 240 = 72X
Subtract 12X from both sides:
240 = 60X
Divide both sides by 60:
4 = X
So Tiffany's running rate is 4 miles per hour.
To find her cycling rate, we substitute the value of X back into the expression X + 20:
4 + 20 = 24
Therefore, Tiffany's cycling rate is 24 miles per hour.
To solve the equation 12/X = 72/(X + 20), we can cross-multiply:
12(X + 20) = 72X
Expanding the left side of the equation:
12X + 240 = 72X
Next, let's move all the X terms to one side and the constant terms to the other side:
240 = 72X - 12X
Combining like terms:
240 = 60X
Now, divide both sides of the equation by 60 to solve for X:
4 = X
So, Tiffany's running rate is 4 miles per hour.
And her cycling rate is X + 20 = 4 + 20 = 24 miles per hour.
Therefore, Tiffany's running rate is 4 miles per hour and her cycling rate is 24 miles per hour.