Question

Aaron and Emma are 260 feet apart when they start walking toward one another. They are walking at the same speed, so whenever Aaron travels

some number of feet, Emma travels the same number of feet. Let x represent the number of feet Aaron has traveled since he started walking toward Emma.


a. Write an expression in terms of that represents the number of feet Aaron has walked toward Emma since they started walking.


b. Write an expression in terms of that represents the number of feet Emma has walked toward Aaron since they started walking.


c. Write an expression in terms of that represents the total number of feet Aaron and Emma have walked toward one another since they started walking


d. Write an expression in terms of that represents the distance in feet) between Aaron and Emma.

Answer 1

The expression that represents Aaron's distance walked, Emma's distance walked, the total distance walked, and the distance between Aaron and Emma.

Step-by-step explanation:

a. The expression that represents the number of feet Aaron has walked toward Emma since they started walking is x feet.

b. The expression that represents the number of feet Emma has walked toward Aaron since they started walking is x feet.

c. The expression that represents the total number of feet Aaron and Emma have walked toward one another since they started walking is 2x feet, because both Aaron and Emma are walking the same distance as each other.

d. The expression that represents the distance between Aaron and Emma is 260 - x feet, because they started 260 feet apart and Aaron has walked x feet.

Answer 2

(a) x

(b) x

(c) 2x

(d) 260-2x

Step-by-step explanation:

The initial and final location of Aaron and Emma has been shown in the figure (a) and (b) respectively.

Let v ft/s be the walking speed of Aaron towards Emma.

As both are moving towards each other at the same speed, so, the walking speed of Emma will be v ft/s towards Aaron.

Let after time,
`t` s, Aaron covered the distance x feet.

As distance= (speed) x (time)

So,
`x=v* t\;\cdots(i)`

(a) The expression for the number of feets Aaron walked towards Emma after time t s is x. [given]

(b) Number of feets Emma walked towards Aaron in the same time
`=v * t`

From equation (i),
`v * t=x`

So, the expression for the number of feets Emma walked towards Aaron is x

(c) The expression for the total number of feet Aaron and Emma have walked toward one another since they started walking is the sum of distance covered by both.

=x+x

=2x

(d) As shown in figure (a), the initial distance between them=260 feet.

Distance covered by them=2x.

The remaining distance between Aaron and Emma is 260-2x feet.

So, the expression that represents the distance between Aaron and Emma is 260-2x feet.