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

Answer:

30 minutes

Step-by-step explanation:

Let

y ---> the distance in miles    

x ---> the time in minutes

Remember that

$1\ h=60\ min$

$766\frac{2}{3}\ mi=\frac{766*3+2}{3}=\frac{2,300}{3}\ mi$

we have the ordered pairs

$(20,\frac{2,300}{3}),(60,2,300)$

Find the slope

$m=(2,300-\frac{2,300}{3})/(60-20)$

$m=(\frac{4,600}{3})/(40)$

$m=\frac{4,600}{120}\\\\m=\frac{115}{3}\ mi/min$  

Find the linear equation in point slope form

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

we have

$m=\frac{115}{3}$

$point\ (60,2,300)$

substitute

$y-2,300=\frac{115}{3}(x-60)$

$y-2,300=\frac{115}{3}x-2,300\\\\y=\frac{115}{3}x$

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

$1,150=\frac{115}{3}x\\\\x=1,150(3)/115\\\\x=30\ minutes$