Question

The shadow of a moon during a solar eclipse travels 2,300 miles in 1 hour. In the first 20 minutes, the shadow traveled 766 and 2/3 miles. How long does it take the shadow to travel 1,150 miles?

Answer 1

It takes approximately 30 minutes for the shadow to travel 1,150 miles during a solar eclipse.

Step-by-step explanation:

To determine the time it takes for the shadow to travel 1,150 miles, we can set up a proportion using the given information. Let's call the time it takes to travel 1,150 miles 't'. We can set up the proportion:

766.67 miles / 20 minutes = 1,150 miles / t

Now, let's solve for 't'. We can cross-multiply:

766.67 * t = 20 * 1,150

Divide both sides by 766.67:

t = (20 * 1,150) / 766.67

Simplifying the right side of the equation gives us:

t ≈ 30

Therefore, it takes approximately 30 minutes for the shadow to travel 1,150 miles.

Answer 2

30 minutes

Step-by-step explanation:

Let

y ---> the distance in miles

x ---> the time in minutes

Remember that

`1\ h=60\ min`

`766(2)/(3)\ mi=(766*3+2)/(3)=(2,300)/(3)\ mi`

we have the ordered pairs

`(20,(2,300)/(3)),(60,2,300)`

Find the slope

`m=(2,300-(2,300)/(3))/(60-20)`

`m=((4,600)/(3))/(40)`

`m=(4,600)/(120)\\\\m=(115)/(3)\ mi/min`

Find the linear equation in point slope form

`y-y1=m(x-x1)`

we have

`m=(115)/(3)`

`point\ (60,2,300)`

substitute

`y-2,300=(115)/(3)(x-60)`

`y-2,300=(115)/(3)x-2,300\\\\y=(115)/(3)x`

Is a proportional relationship between the variables x and y (speed)

For y=1,150 miles

substitute the value of y in the linear equation and solve for x

`1,150=(115)/(3)x\\\\x=1,150(3)/115\\\\x=30\ minutes`