An airplane travels 1260km in the same time a car travels 429km. If the rate of the car is 120kph less than the rate of the airplane, find the rate of each.
rate of plane --- x km/h
rate of car ------ x-120 km/h
time for plane = 1260/x
time for car = 429/(x-120)
1260/x = 429/(x-120)
cross- multiply ....
1260(x-120) = 429x
carry on
To solve this problem, we can use the formula: time = distance / speed.
Let's assume the rate (speed) of the airplane is x km/h.
According to the problem, the rate of the car is 120 km/h less than the rate of the airplane. Therefore, the rate of the car is (x - 120) km/h.
Now, let's calculate the time it takes for the airplane and the car to travel their respective distances:
For the airplane:
time_airplane = distance_airplane / speed_airplane
For the car:
time_car = distance_car / speed_car
Given that the distance traveled by the airplane is 1260 km, and the distance traveled by the car is 429 km, we can write the equations as follows:
time_airplane = 1260 / x
time_car = 429 / (x - 120)
According to the problem, the time taken by the airplane and the car is the same. Therefore, we can set these two equations equal to each other:
1260 / x = 429 / (x - 120)
To solve for x, we can cross-multiply:
1260(x - 120) = 429x
Now, let's simplify the equation:
1260x - 151200 = 429x
Subtract 429x from both sides:
831x - 151200 = 0
Now add 151200 to both sides:
831x = 151200
Divide both sides by 831:
x = 182
So, the rate (speed) of the airplane is 182 km/h.
Now substitute this value back into one of the equations to find the speed of the car:
speed_car = speed_airplane - 120
speed_car = 182 - 120
speed_car = 62 km/h
Therefore, the rate of the car is 62 km/h.