Samantha 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?
D = RT (Distance = Rate x Time)
R = rate of bike
0.67 = time of bike (2/3 = 0.67)
0.67R = distance of bike
R + 12 = rate of car
0.33 = time of ca (1/3 = 0.33)
.33(R + 12) = distance of car
Since distance is equal
0.67R = 0.33(R + 12)
Solve for R, rate of bike
To find out how fast Samantha rides her bike, we need to use the information given in the problem.
Let's assume the speed at which Samantha rides her bike is "x" miles per hour.
According to the problem, Samantha can ride her bike to work in 2/3 of an hour. This means she covers the distance from her home to work in 2/3 hours riding her bike. So, the distance is given by (2/3) * x = (2/3)x miles.
We also know that when she drives to work, it takes her 1/3 of an hour (1/3 hour) to cover the same distance. Since she is driving, her speed will be x + 12 miles per hour (because she drives 12 miles per hour faster than she rides her bike). So, the distance covered when driving is (1/3) * (x + 12) = (1/3)(x + 12) miles.
As per the problem, both distances are the same (since they represent the distance from her home to work), so we can set up an equation:
(2/3)x = (1/3)(x + 12)
Simplifying the equation, we multiply both sides by 3 to remove the denominators:
2x = x + 12
Now, we can solve for x by subtracting x from both sides:
x = 12
Therefore, Samantha rides her bike at a speed of 12 miles per hour.