Both Al and Bill must run from their positions to point C and then on to D. They start at the same time and each runs at a constant speed . When Bill gets to point C Al has passed there and is 40 yards towards D. If point D is ____ yards from C, they will arrive at point D at the same time.

To find the distance from point C to point D, we need to determine the relative speeds and positions of Al and Bill.

Let's assume Al's speed is v yards per second. Since Bill starts running at the same time as Al, we can also assume Bill's speed is v yards per second.

When Bill reaches point C, Al has already passed that point and is 40 yards towards point D. This means that Al has covered an extra distance of 40 yards compared to Bill.

To keep things simple, let's consider the time it takes for Bill to reach point C as t seconds. Al, who is running at the same speed, will also take t seconds to travel from point C to the 40 yards past C.

So, if Bill's speed is v yards per second and he takes t seconds to reach point C, the distance BC is v * t yards.

Since Al passes C and runs an additional 40 yards, the total distance AD is BC + 40 yards, which can be expressed as (v * t) + 40 yards.

Now, we know that the time it takes for Al to run from C to the 40 yards past C is also t seconds. Therefore, Al's speed can be calculated as the distance (40 yards) divided by the time (t seconds). This gives us Al's speed as 40 / t yards per second.

For Al to cover the distance AD, it would take him ((v * t) + 40) / (40 / t) seconds. Simplifying the expression, we get:

((v * t) + 40) / (40 / t) = (v * t^2 + 40) / 40

Now, since Al and Bill arrive at point D at the same time, we know that the time it takes for Bill to run from point C to D is the same as the time it takes for Al to run from the 40 yards past C to D.

The distance CD is the same for both Al and Bill, so we can write:

CD / v = ((v * t^2 + 40) / 40) / v

Simplifying further, we have:

CD = (v * t^2 + 40) / 40

This equation tells us that the distance from point C to point D, denoted as CD, can be calculated using the values of the speed v and the time t.