Two cars traveled equal distances in different amounts of time. Car A traveled the distance in 4 h, and Car B traveled the distance in 4.5 h. Car B traveled 5 mph slower than Car A.
(The formula R⋅T=D , where R is the rate of speed, T is the time, and D is the distance can be used.)
How fast did Car B travel?
Let's assume that Car A traveled at a speed of x mph.
Since Car B traveled 5 mph slower than Car A, Car B's speed can be expressed as (x-5) mph.
The distance traveled by both cars is equal.
Using the formula R⋅T=D, the distance traveled by Car A is x * 4 = 4x.
The distance traveled by Car B is (x-5) * 4.5 = 4.5x - 22.5.
Since both cars traveled the same distance, we can set up the equation:
4x = 4.5x - 22.5
To solve for x, let's subtract 4x from both sides of the equation:
0.5x = 22.5
Then, divide both sides of the equation by 0.5:
x = 45
Therefore, Car A traveled at a speed of 45 mph.
To find Car B's speed, we subtract 5 from Car A's speed:
45 - 5 = 40.
Therefore, Car B traveled at a speed of 40 mph.
Let's assume that the rate of speed of Car A is R mph.
According to the information given, Car B traveled 5 mph slower than Car A. So, the rate of speed of Car B can be expressed as (R - 5) mph.
We know that distance (D) equals rate (R) multiplied by time (T).
For Car A, distance = R * 4 h
For Car B, distance = (R - 5) * 4.5 h
Since both cars traveled the same distance, we can set these two distances equal to each other:
R * 4 = (R - 5) * 4.5
Now, let's solve this equation to find the value of R:
4R = 4.5(R - 5)
Distributing 4.5 on the right side:
4R = 4.5R - 22.5
Subtracting 4.5R from both sides:
-0.5R = -22.5
Dividing both sides by -0.5:
R = 45
Therefore, Car A traveled at a speed of 45 mph.
Since Car B traveled 5 mph slower, the speed of Car B can be calculated as:
Speed of Car B = Car A's speed - 5
= 45 - 5
= 40 mph
Therefore, Car B traveled at a speed of 40 mph.
To find the speed of Car B, we first need to determine the distance traveled by both cars. We know that Car A traveled the distance in 4 hours, and Car B traveled the same distance in 4.5 hours.
Using the formula R⋅T=D, we can write two equations:
For Car A: R_A⋅4 = D
For Car B: R_B⋅4.5 = D
We also know that Car B traveled 5 mph slower than Car A. So, we can write another equation:
R_B = R_A - 5
Now, we can substitute the value of D from the first equation into the second equation:
R_B⋅4.5 = R_A⋅4
Substituting the value of R_B from the third equation:
(R_A - 5)⋅4.5 = R_A⋅4
Expanding the equation:
4.5R_A - 22.5 = 4R_A
Simplifying:
0.5R_A = 22.5
Dividing by 0.5:
R_A = 45
Therefore, Car A traveled at a speed of 45 mph.
Substituting this back into the third equation to find the speed of Car B:
R_B = R_A - 5
R_B = 45 - 5
R_B = 40
So, Car B traveled at a speed of 40 mph.