Question

Wanda started walking along a path 27 seconds before Dave. Wanda walked at a constant rate of 3 feet per second. Dave walked along the same path at a constant rate of 4.5 feet per second. Graph the system of linear equations. How long after Dave starts walking will he catch up with Wanda?

Answer 1

Wanda and Dave will catch each other in 54 seconds after Dave starts walking.

Explanation:

Let Wanda and Dave catch each other when x be the time after Dave starts walking and y be the distance covered by them

It is given that Wanda started walking along a path 27 seconds before Dave and the constant speed of Wanda is 3 feet per second.

`speed=(distance)/(time)`

`3=(y)/(x+27)`

`y=3(x+27)`

`y=3x+81` .... (1)

The constant speed of Dave is 4.5 feet per second.

`4.5=(y)/(x)`

`y=4.5x` .... (2)

Equate equation (1) and (2).

`3x+81=4.5x`

`81=1.5x`

Divide both sides by 1.5.

`(81)/(1.5)=x`

`54=x`

Therefore, Wanda and Dave will catch each other in 54 seconds after Dave starts walking.