Question 1162431
rate * time = distance.
let x equal the rate that mattie travels at.
let y equal the rate that the plane travels at.
let z = the time
for the car, the formula becomes x * z = 250
for the plane, the formula becomes y * z = 1200
you are given that the rate of the plane is 190 miles per hour faster than the rate of the car.
this means y = x + 190
the formulas become:
x * z = 250
(x + 190) * z = 120
simplify the second equation and leave the first equation as is to get:
x * z = 250
x * z + 190 * z = 1200
subtract the first equation from the second to get:
190 * z = 950
solve for z to get:
z = 5
that's the time the the car and the plane took.
for the car, x * z = 250 becomes x * 5 = 250.
solve for x to get x = 50 miles per hour.
y = x + 190 makes y = 240 miles per hour.
for the car, the formula becomes:
5 * 50 = 250 miles
for the plane, the formula becomes:
5 * 240 = 1200 miles
solution looks good.
solution is that the speed of the plane is 240 miles per hour.