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 firstvcar is 14 miles per hour faster than the speed of the second car, find the speed of both cars. (Source:Top Ten of Everything)
its simple ratio
if
car A miles car B miles
224 : 14 :: 175 : y or y
14:175 :: 224:y
or 14x175=224xy
2450=224y
2450/224=y
10.9375=y
or y=10.9375
or y=11 miles per hour (rounding)
Note: do the calculation again
To find the speed of each car, we can set up a system of equations based on the given information.
Let's denote the speed of the second car as 'x' miles per hour. Since the speed of the first car is 14 miles per hour faster, we can represent it as 'x + 14' miles per hour.
We know that time is constant for both cars. So, we can use the formula:
time = distance / speed
For the first car, the distance is 224 miles and the speed is 'x + 14' miles per hour. Therefore:
224 / (x + 14) = t
For the second car, the distance is 175 miles and the speed is 'x' miles per hour. Therefore:
175 / x = t
Since both cars take the same time, we can set these two equations equal to each other:
224 / (x + 14) = 175 / x
Now, we can cross multiply to solve for x:
224 * x = 175 * (x + 14)
Simplifying:
224x = 175x + 2450
Subtracting 175x from both sides:
49x = 2450
Dividing both sides by 49:
x = 50
So, the speed of the second car is 50 miles per hour.
To find the speed of the first car, we can substitute this value back into one of the equations. Let's use the first equation:
224 / (x + 14) = t
224 / (50 + 14) = t
224 / 64 = t
t = 3.5
Therefore, the speed of the first car is:
x + 14 = 50 + 14 = 64 miles per hour.
Hence, the speed of the first car is 64 miles per hour, and the speed of the second car is 50 miles per hour.