An airplane travels 1260km in the same time a car travels 420km. If the rate of the car is 120kph less than the rate of the airplane, find the rate of each.
looks like the same problem I just solved for you except you changed one number.
Repeat my steps
To solve this problem, let's assume the rate of the airplane is represented by 'x' km/h. Since the rate of the car is 120 km/h less than the rate of the airplane, the rate of the car is 'x - 120' km/h.
We are given that the airplane travels 1260 km in the same time it takes the car to travel 420 km. Let's denote the time it takes for both vehicles to travel these distances as 't' hours.
Using the formula distance = rate * time:
For the airplane: 1260 = x * t
For the car: 420 = (x - 120) * t
Now we have a system of two equations with two unknowns. We can solve this system to find the values of 'x' and 't'.
Dividing the first equation by the second equation:
1260 / 420 = (x * t) / ((x - 120) * t)
Simplifying:
3 = x / (x - 120)
Cross-multiplying:
3(x - 120) = x
Expanding and rearranging:
3x - 360 = x
2x = 360
x = 180
Therefore, the rate of the airplane is 180 km/h, and the rate of the car is 180 - 120 = 60 km/h.