Question

Robin is standing on the top of a 40-foot flagpole at 1 p.m. At the same time, a 4-foot child on the ground casts a shadow of length 0.8 feet. If Robin is 6 feet tall, how much longer is the shadow of the flagpole and Robin together than the shadow of the flagpole alone? Specify your answer as a decimal to the nearest tenth.

Answer 1

1.2

Explanation:

The height of an object and the length of its shadow are directly proportional. Let h be the height of an object and s be the length of its shadow. From the information about the child, we have h/s = 4/(0.8) = 5. The flagpole with Robin on top has a height of 46 feet. Suppose its shadow has length x. Solving the equation 46/x = 5 for x gives us x = 46/5 = 9.2 feet. The flagpole alone is 40 feet tall. Suppose its shadow has length $y.$ Then, we must have 40/y = 5. Solving this equation gives y=8 feet. So, the difference in shadow lengths is 9.2 -8= 1.2

Answer 2

1.2 ft

Explanation:

We can use ratio's to solve this problem. Put the item on top, and the shadow on the bottom

40 ft flagpole 4 ft child

--------------------- = --------------------

x ft shadow .8 ft shadow

Using cross products

40 * .8 = 4x

32 = 4x

Divide each side by 4

32/4 = 4x/4

8 = x

The flag pole casts an 8 ft shadow

The question asks how much longer is the shadow of the flagpole and Robin than the flagpole? In other words, how long is Robins shadow

40 ft flagpole 6ft Robin

--------------------- = --------------------

8 ft shadow x ft shadow

Using cross products

40 *x = 6*8

40x = 48

Divide by 40

40x/40 = 48/40

x = 1.2