Currently, the Toyota Corolla is the best selling car in the world. Suppose that during a test drive of two Corollas, one car travels 224 miles in the same time that the second car travels 175 miles. If the speed of the first car is 14 miles per hour faster than the speed of the second car, find the speed of both cars.
speed x time = distance
let v be the speed of the second car
We know that:
(v+14) x t = 224
and
v x t = 175
Let's isolate t for both equations. You get:
t = 224 / (v+14)
and
t = 175 / v
We know that t is the same for both, so:
224 / (v+14) = 175 / v
Cross multiply.
224v = 175(v+14)
224v = 175v + 2450
Collect like terms:
49v = 2450
v = 50
Therefore, the speed of the first car is (50+14) = 64 mph, while the speed of the second car is 50 mph.
To find the speed of both cars, we will first set up a system of equations based on the information given.
Let's assume the speed of the second car is "x" miles per hour.
According to the problem, the speed of the first car is 14 miles per hour faster than the speed of the second car. Therefore, the speed of the first car is "x + 14" miles per hour.
Now, we will use the formula "speed = distance / time" to form two equations.
For the first car (car 1):
Speed of car 1 = (x + 14) mph
Distance traveled by car 1 = 224 miles
Time taken by car 1 = unknown (let's call it t hours)
Therefore, the equation for car 1 becomes:
(x + 14) = 224 / t
For the second car (car 2):
Speed of car 2 = x mph
Distance traveled by car 2 = 175 miles
Time taken by car 2 = unknown (also t hours)
Therefore, the equation for car 2 becomes:
x = 175 / t
Now, we have a system of two equations:
(x + 14) = 224 / t
x = 175 / t
To solve this system of equations, we can use the method of substitution.
Rearrange the first equation to solve for t:
t = 224 / (x + 14)
Substitute this expression for t in the second equation:
x = 175 / (224 / (x + 14))
Now, let's simplify the equation:
x = 175 * (x + 14) / 224
Multiply both sides by 224 to eliminate the denominator:
224x = 175 * (x + 14)
Expand:
224x = 175x + 2450
Rearrange the equation:
49x = 2450
Divide both sides by 49:
x = 2450 / 49
Calculate the value of x:
x ≈ 50
Therefore, the speed of the second car is approximately 50 mph.
To find the speed of the first car, substitute this value of x into one of the equations:
(x + 14) = 224 / t
(50 + 14) = 224 / t
64 = 224 / t
Now, solve for t:
t = 224 / 64
t ≈ 3.5
Therefore, the speed of the first car is approximately 64 mph.
So, the speed of the first car is 64 mph and the speed of the second car is 50 mph.