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A 10-speed bike changes gears by moving the chain to different size sprockets on the front and back. The speed at which the bike goes varies directly with the number of revolutions per minute (rpm) you turn the pedals, directly with the number of teeth on the front sprocket, and inversely with the number of teeth on the back sprocket. A standard bike with 70 cm diameter wheels will go about 7.4 kilometers per hour if you pedal 40 rpm in the lowest gear (39-tooth front sprocket, 28-tooth back one). Write an equation expressing km/h in terms of the three independent variables.

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MrRoyal

The variation is a joint variation, and the equation that relates the three independent variables is [tex]s = 0.18\frac{rf}{b}[/tex]

How to determine the equation in terms of the variables?

The direct and the inverse variations from the question can be represented using:

[tex]s = k\frac{rf}{b}[/tex]

Where:

  • s represents the speed; s = 10
  • k represents the constant of variation
  • r represents the number of revolutions per minute
  • f represents the number of front sprocket teeth
  • b represents the number of back sprocket teeth

From the question, we have:

r = 40; f = 39; b = 28

So, we have:

[tex]s = k\frac{rf}{b}[/tex]

[tex]10 = k\frac{40 * 39}{28}[/tex]

Make k the subject

[tex]k = \frac{10 * 28}{40 * 39}[/tex]

Evaluate

k = 0.18

Substitute k = 0.18 in [tex]s = k\frac{rf}{b}[/tex]

[tex]s = 0.18\frac{rf}{b}[/tex]

Hence, the equation that relates the three independent variables is [tex]s = 0.18\frac{rf}{b}[/tex]

Read more about variation at:

https://brainly.com/question/6974617

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