Question

. Two people are standing next to each other on horizontal ground. One is 5 feet tall, and the other is 6 feet tall. The shadow of the person who is 6 feet tall is 3 feet shorter than twice the length of the shadow of the person who is 5 feet tall. How long is the shorter person’s shadow? Show work, and express your answer using a complete sentence including units.

Answer 1

Answer: 3.75

Explanation:

Answer 2

3.75 feet.

Explanation:

Given:

Two people are standing next to each other on horizontal ground.

One is 5 feet tall, and the other is 6 feet tall.

The shadow of the person who is 6 feet tall is 3 feet shorter than twice the length of the shadow of the person who is 5 feet tall.

Question asked:

How long is the shorter person’s shadow?

Solution:

Let the shadow 5 feet person =
`x`

As given, shadow of 6 feet person is 3 feet shorter than twice the length of the shadow of 5 feet person.

Then, the shadow 6 feet person =
`2x-3`

Now, as we know:

Ratio of the shadow of two objects are in proportion of their heights, so:-

`(Shadow\ of\ 5\ feet \ person)/(Shadow\ of\ 6\ feet\ person)=(5)/(6)`

=
`(x)/(2x-3) =(5)/(6)`

By cross multiplication:

`6* x=5*(2x-3)\\\\6x=10x-15`

Subtracting both sides by
`10x`

`6x-10x=10x-10x-15\\-4x=-15\\`

Adding both sides by minus

`4x=15`

Dividing both sides by 4

`x=(15)/(4)`

`x=3.75\ feet`

shadow 5 feet person =
`x` = 3.75 feet

Therefore, shadow of the shorter person is 3.75 feet.