Two cars lost in a blinding snowstorm are traveling across a large field, each thinking they are on the road, as shown in the figure on the left. They collide. If the distance x is 141 meters and the red car is travelling at 19.5 mph, how fast to the nearest hundredth of a mph was the blue car travelling? (As unlikely as this event seems it actually happened to the problem author's wife.)

which car has to cover distance x?

time = distance/speed

no diagram to refer to here.

To determine the speed of the blue car, we can apply the concept of relative velocity. Relative velocity refers to the velocity of one object as observed from the frame of reference of another object.

In this scenario, let's consider the frame of reference of the red car. From the perspective of the red car, the blue car appears to be moving towards it. To find the speed of the blue car relative to the red car, we need to subtract the velocity of the red car from the combined velocity of the two cars at the time of collision.

Let's convert the speed of the red car from miles per hour (mph) to meters per second (m/s) for consistency. 1 mile = 1609.34 meters and 1 hour = 3600 seconds.

Speed of the red car = 19.5 mph = (19.5 * 1609.34) / 3600 m/s = 8.723 m/s (rounded to three decimal places).

Now, we can determine the combined velocity of the two cars at the time of collision. Since they collide, their total distance covered would be equal to the sum of their individual distances:

Distance = Velocity * Time

Assuming the time taken to collide is the same for both cars, the blue car would cover a distance of x meters as well. Let the speed of the blue car be denoted by V_blue.

Distance covered by the red car = Velocity of the red car * Time = 8.723 m/s * Time

Distance covered by the blue car = V_blue * Time = V_blue * Time

Since the total distance covered is x, we can write the equation:

8.723 m/s * Time + V_blue * Time = x

Rearranging the equation to solve for V_blue:

V_blue * Time = x - 8.723 m/s * Time

V_blue = (x - 8.723 m/s * Time) / Time

Given that x = 141 meters, we can substitute that value into the equation:

V_blue = (141 m - 8.723 m/s * Time) / Time

At this point, we need additional information to proceed. We would require either the value of Time or any other relation between Time and V_blue to calculate the speed of the blue car accurately.

If you have any additional information, please provide it so that we can continue solving the problem.