A plane can fly 980 miles in the same time as it takes a car to go 420 miles. If the car travels 80 mph slower than the plane, find the speed of the plane.
p = plane speed
car speed = p-80
time = distance / speed
980 / p = 420 / (p-80)
(p-80)(980) = 420 p
980 p - 420 p = 80 * 980
560 p = 80 * 980
56 p = 80 * 98
28 p = 80 * 49
4 p = 80 * 7
p = 20 * 7 = 140 mph
980/280100
Why did the plane and the car start a race? Because they wanted to find out who's faster! Well, it looks like the plane is quite the speed demon. Let's do some math to figure out its speed.
Let's call the speed of the plane "P" and the speed of the car "C". We know that the plane can fly 980 miles in the same time it takes the car to travel 420 miles. So, we can set up the equation:
980 / P = 420 / C
We also know that the car travels 80 mph slower than the plane, so we can express the car's speed in terms of the plane's speed:
C = P - 80
Now, let's substitute this expression for C in our equation:
980 / P = 420 / (P - 80)
To solve this equation, we can cross-multiply:
980(P - 80) = 420P
Now, let's simplify and solve for P:
980P - 78400 = 420P
560P = 78400
P = 78400 / 560
P ≈ 140
So, the speed of the plane is approximately 140 mph. Watch out, car, here comes the speedy plane!
Let's assume the speed of the car is 'x' mph.
Since the car is traveling 80 mph slower than the plane, the speed of the plane can be represented as 'x + 80' mph.
We know that time = distance / speed.
The time it takes for the plane to travel 980 miles is:
Time for the plane = distance / speed = 980 / (x + 80) hours
The time it takes for the car to travel 420 miles is:
Time for the car = distance / speed = 420 / x hours
According to the given information, both of these times are equal. Therefore, we can equate them:
980 / (x + 80) = 420 / x
To remove the fractions, we can cross-multiply:
980x = 420(x + 80)
Simplifying further:
980x = 420x + 33600
Subtracting 420x from both sides:
560x = 33600
Dividing both sides by 560:
x = 60
So, the speed of the car is 60 mph.
The speed of the plane is 60 + 80 = 140 mph.
To find the speed of the plane, we can set up a proportion based on the given information.
Let's say the speed of the plane is x mph.
Since the car travels 80 mph slower than the plane, the speed of the car is (x - 80) mph.
The time taken by the plane to travel 980 miles is the same as the time taken by the car to travel 420 miles.
The formula for time is distance divided by speed.
For the plane: time = distance / speed = 980 / x
For the car: time = distance / speed = 420 / (x - 80)
Since the times are the same, we can set up an equation:
980 / x = 420 / (x - 80)
To solve for x, we can cross-multiply:
980(x - 80) = 420x
980x - 78400 = 420x
Subtract 420x from both sides:
980x - 420x - 78400 = 0
560x - 78400 = 0
Add 78400 to both sides:
560x = 78400
Divide both sides by 560:
x = 78400 / 560
x = 140
Therefore, the speed of the plane is 140 mph.