The stopping distance d of a car after the brakes are applied varies directly as the square of the speed r. If a car travelling 70mph can stop in 270ft, how many feet will it take the same car to stop when it is travelling 60mph?

Thank you.

Well, well, well, looks like we have ourselves a math problem! Let's put on our thinking caps and tackle this one.

We know that the stopping distance varies directly as the square of the speed. So, if we let d represent the stopping distance and r represent the speed, we can write the proportional relationship as: d = k * r^2.

Now we have some juicy information: when the car is going 70mph, it stops in 270ft. So we can plug those values into our equation: 270 = k * 70^2.

Now let's find out what this mysterious constant k is. Divide both sides of the equation by 4900 (because 70^2 = 4900): k = 270/4900.

Now we can use our newly discovered k to find out how many feet it will take for the car to stop when traveling at 60mph. We'll call this stopping distance d2: d2 = k * 60^2.

But wait, we know what k is! So we can substitute it back into the equation: d2 = (270/4900) * 60^2.

Calculating the right-hand side, we get d2 = 216ft.

So, if my math skills haven't failed me, it will take the car 216ft to stop while traveling at 60mph. Just remember, always practice safe stopping distances, and never forget that I'm here to entertain you with my mathematical comedy skills!

To solve this problem, we need to use the concept of direct variation.

Direct variation means that two quantities, in this case, the stopping distance (d) and the square of the speed (r^2), are directly proportional to each other. Mathematically, we can write this as:

d = k * r^2

Where k is the constant of variation.

Given that a car traveling at 70mph has a stopping distance of 270ft, we can plug these values into the equation to find the value of k:

270 = k * 70^2

Simplifying the equation, we have:

270 = k * 4900

Next, solve for k by dividing both sides of the equation by 4900:

k = 270 / 4900
k = 0.0551

Now that we have the value of k, we can use it to find the stopping distance (d) when the car is traveling at 60mph. Plugging in the values into the equation:

d = 0.0551 * 60^2

Using a calculator, simplify the equation:

d ≈ 198.36

Therefore, it would take approximately 198.36 feet for the car to stop when it is traveling at 60mph.