Question

Some friends are going on a coaster ride at an amusement park. They board their car on a platform that is 10 1/4 feet above the ground. The car starts by going up 80 1/4 feet. Then the car goes down 70 1/2 feet and comes to a stop. What is the change in height from where the friends started on the platform to where they are when the car stops?

Answer 1

The given question can be exemplified in the following diagram:

We are asked to determine the change in height. To do that we need to have into account that the sum of the change in height and the height the car goes down before stopping equals the total height the car went up, this can be expressed mathematically as follows:h

`CH+70\text{ 1/2 = 80 1/4}`

Now we solve for the change in height by subtracting 70 1/2 from both sides of the equation:

`CH=80\text{ 1/4 - 70 1/2}`

Now we rewrite the mixed fraction into their integer and fractional parts as follows:

`CH=80+(1)/(4)-70-(1)/(2)`

Now we subtract the integer parts:

`CH=10+(1)/(4)-(1)/(2)`

Now we subtract the fractions:

`CH=10-(1)/(4)`

Now we solve the operation:

`CH=(39)/(4)`

This can be rewritten as:

`CH=(36+3)/(4)`

We can separate the denominator:

`CH=(36)/(4)+(3)/(4)`

Simplifying the first fraction:

`CH=9+(3)/(4)`

This can be rewritten as a mixed fraction:

`CH=9\text{ 3/4}`

Therefore, the change in height is 93