Question 638073
they're 5 miles apart.
they will meet for dinner in 1/2 hour.
the dinner place is located between them.
they leave their homes at the same time.
dave walks 2 miles per hour faster than kyle.
they both arrive at the dinner place in 30 minutes.


let the rate that kyle walks be x miles per hour.
this means the rate that dave walks is x+2 miles per hour.


the basic formula is rate * time = distance.


since 30 minutes is equal to .5 hours, we'll use rate in miles per hour and time in hours.


kyle walks x miles per hour for 30 minutes.
dave walks x+2 miles per hour for 30 minutes.


the diner is located somewhere between them but we don't know exactly where.
the distance between them is 5 miles.


assume kyle walks y miles.
this means that dave must walk 5-y miles.


the equation for kyle is based on rate * time = distance and becomes:
.5x = y


the equation for kyle is .5x = y
the equation for dave is .5(x+2) = 5-y


these are 2 equation that need to be solved simultaneously.
the easiest way to do that is the substitute for y from the first equation into the second equation.


after substituting .5x for y, the second equation becomes:
.5(x+2) = 5 - .5x
simplify this equation to get:
.5x + 1 = 5 - .5x
subtract 1 from both sides of the equation and add .5x to both sides of the equation to get:
x = 4
this means that x+2 = 6


kyle is walking 4 miles per hour and dave is walking 6 miles per hour.


kyle walks 4 miles per hour for 1/2 hour for a total of 2 miles.
dave walks 6 miles per hour for 1/2 hour for a total of 3 miles.


the diner is 2 miles from kyle's house and 3 miles from dave's house.


you had 2 equations with 2 unknown variables each.
substituting from 1 equation into the other equation left you with 1 equation with 1 unknown.
this could be solved and that led to the value of x.
once x was found, the rest could be found without too much difficulty.