To reach a vacation spot, the Jones family first traveled by plane and then drove the remaining distance in a?

To reach a vacation spot, the Jones family first traveled by plane and then drove the remaining distance in a rented car. The distance by car was 125 kilometers less than the distance by plane.The total distance was 500 kilometers less than three times the distance traveled by car. Find the distance flown in the airplane.

Let c = distance by car and p = distance by plane, then
c = p - 125
The total distance is the distance by car plus the distance by plane, so the total distance equals c + p.
Also, you are given that the total distance is 500 less than 3 times the distance by car, so you have
c + p = 3c - 500
Solve for p in the first equation
p = c + 125
Replace p with c + 125 in the second equation
c + c + 125 = 3c - 500
Combine like terms
2c + 125 = 3c - 500
Subtract 3c from each side
-c + 125 = - 500
Subtract 125 from each side
-c = -625
Divide each side by -1
c = 625
Replace c with 625 in the equation p = c + 125 to find p.
p = 625 + 125
p = 750

There are two equations here:
x+(x-125) = Y
and
Y = 3*(x-125) - 500
x+(x-125) = 3*(x-125) - 500
2x - 125 = 3*(x-125) - 500
2x + 375 = 3x - 375
2x + 750 = 3x
x = 750

Two equations, two unknowns.
X = distance by plane
Y = total distance

There are two equations here:
Y= X + (X-125)
and
Y = 3 * (X-125) - 500

OR

X + (X-125) = 3 * (X-125) - 500

2X - 125 = 3X - 375 - 500 (take X to one side, numbers to the other)

750 = X; X = 750

The plane went 750 km, the car 750km-125km = 625km, the total distance, 750km + 625km = 1375km. total to reach the vacation spot.

The distance flown by the airplane was 750km.

It took them nine hours and 59 minutes to fly because they had a layover in denver and in Houston, and then 20 hours to drive the 625 km because they had to drive through Mexico, and the roads in Mexico are slower, and they got stopped in Customs because they didn't have any insurance on their rented car.

Do your own home work!