The diameter of each tire on Niki's bike is 66 centimeters (cm). It takes her 16 minutes to ride 10 kilometers (km).

How fast did Niki ride, in kilometers per hour?

Let's use a proportion. Cross multiply and solve for x.

16/10 = 60/x

16x = 600

x = 600/16

x = 37.5 km/h

37.5

To find Niki's speed in kilometers per hour, we need to first convert the given information into a common unit of measurement.

First, let's convert the diameter of each tire from centimeters to meters. Since there are 100 centimeters in a meter, we can divide the diameter by 100 to get the measurement in meters:

66 cm ÷ 100 = 0.66 meters

Next, we need to find the circumference of the tire. The circumference can be calculated using the formula:

Circumference = π × Diameter

where π (pi) is a constant value approximately equal to 3.14159.

Plugging in the diameter we found:

Circumference = 3.14159 × 0.66 = 2.07577 meters

Now that we know the circumference of the tire, we can find the distance Niki travels with each revolution of the tire. Since the circumference represents the distance traveled in one revolution, we have:

Distance per revolution = Circumference = 2.07577 meters

To find out how many revolutions Niki needs to complete to travel 10 kilometers, we convert 10 kilometers to meters:

10 km × 1000 = 10,000 meters

Now, we can divide the total distance by the distance per revolution to find the number of revolutions:

Number of revolutions = 10,000 meters ÷ 2.07577 meters = 4,822.37 revolutions

Since there are two tires on Niki's bike and each revolution represents the distance traveled by one tire, we can find the total number of revolutions made by both tires:

Total revolutions = 4,822.37 revolutions × 2 = 9,644.74 revolutions

Now we have all the necessary information to calculate the speed in kilometers per hour. We know that Niki completes 9,644.74 revolutions in 16 minutes. To convert this time to hours, we divide by 60:

16 minutes ÷ 60 = 0.2667 hours

Finally, we can calculate the speed:

Speed = Total distance / Time

Speed = 10 km ÷ (0.2667 hours) = 37.498 km/h

Therefore, Niki rode at a speed of approximately 37.498 kilometers per hour.