Ashley can ride her bike to work in 2/3 of an hour. When she drives to work it takes 1/3 of an hour. If she drives 12 miles per hour faster than she rides her bike, how fast does she ride her bike?
Let x = bike speed and x+12 = car speed. Since they both go the same distance:
2/3x = 1/3(x+12)
Solve for x.
To find out how fast Ashley rides her bike, let's assume the speed at which she rides her bike is represented by the variable 'x' (in miles per hour).
First, let's calculate the time it takes for Ashley to drive to work: 1/3 of an hour.
Next, let's determine the distance she travels when driving to work. We know the formula speed = distance/time. Since she drives 12 miles per hour faster than she rides her bike, the speed at which she drives is (x + 12) miles per hour. Plugging in the values, we get:
speed = distance/time
(x + 12) = distance/(1/3)
Since the given time is expressed in 1/3 of an hour, we can rewrite this as:
(x + 12) = distance/(1/3)
(x + 12) = 3 * distance
Now, let's calculate the time it takes for Ashley to ride her bike to work: 2/3 of an hour.
Next, let's determine the distance she travels when riding her bike. We use the same formula:
speed = distance/time
x = distance/(2/3)
x = 3 * distance
Now, we have two equations:
(x + 12) = 3 * distance
x = 3 * distance
To solve this system of equations, we can equate the right sides of the equations:
(x + 12) = x
Simplifying this equation, we get:
12 = 0
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