Solve algebraically using systems of equations Begin by defi

Solve algebraically using systems of equations: Begin by defining the variables together with the units of measure . 3) Two cars leave town, one traveling east and the other west. After 3 hours they are 297 miles apart. If one car is traveling 5 mph faster than the other, what is the speed of each?

Solution

Given

there are 2 cars moving in opposite directions (one in east and other in west)

let the speed of one car be \"x\" miles/hr

and speed of other car be \"y\" miles /hr

it is given that one car travels 5 mph faster then the other

therefore

y = x + 5           (1)

Given

After 3 hours they are 297 miles apart

so both the cars have travelled for 3 hours

and total distance between them = 297 miles

distance travelled by car moving with speed of \"x\" miles/hr = speed * time

                                                                = x * 3 = 3x      // distance = speed * time

distance travelled by car moving with speed of \"y\" miles/hr = speed * time

                                                                            = y * 3 = 3y miles

so the distance trvalled by both should be 297 miles (as they are 297 miles away)

3x +3y = 297           //divide both sides by \"3\"

x + y = 99                    (2)    

x+y = 99   

x + (x+5) = 99              from(1) y= x+5

2x + 5 =99

2x = 94

x = 47

therefore y =x+5 => 47 +5 = 52              

therefore the speed of cars = 47 miles/hr and 52 miles/hr