Two cars traveled equal distances in different amounts of time. Car A traveled the distance in 2.4 h, and Car B traveled the distance in 4 h. Car A traveled 22 mph faster than Car B.
How fast did Car A travel?
_______MPH
distancea=timea*speeda
distanceb=timeb*speedb
setting them equal
timea*speeda=timeb*speedb
you are given the two times, and speeda=speedb+22
so
2.4*(speedb+22)=4*speedb
with a little manipulation
speedb(2.4-4)=-2.4*22
speedb=you can do it.
I hav ccbfv
To find the speed of Car A, we first need to calculate the speed of Car B. We know that Car B traveled the distance in 4 hours.
Let's assume the speed of Car B is x mph.
Therefore, using the formula Speed = Distance / Time, we can write the equation for Car B as:
x = Distance / Time
Since both cars traveled the same distance, we can set the distance equal for both cars. This gives us:
Distance = Distance
Therefore, we can write another equation for Car A's speed:
Car A's speed = Car B's speed + 22 mph
Now let's solve for the speed of Car A.
Since Car B traveled at a speed of x mph for 4 hours, the total distance traveled by Car B is:
Distance = Speed x Time
Distance = x mph x 4 hours = 4x miles
Similarly, Car A traveled the same distance but in a shorter time of 2.4 hours. So the total distance traveled by Car A is:
Distance = Speed x Time
Distance = (x + 22) mph x 2.4 hours = 2.4(x + 22) miles
Since both cars covered the same distance, we can set the equations equal to each other:
4x = 2.4(x + 22)
Now let's solve for x, the speed of Car B:
4x = 2.4x + 52.8
4x - 2.4x = 52.8
1.6x = 52.8
x = 52.8 / 1.6
x = 33
So the speed of Car B is 33 mph.
Now let's find the speed of Car A by adding 22 to Car B's speed:
Car A's speed = Car B's speed + 22 mph
Car A's speed = 33 mph + 22 mph
Car A's speed = 55 mph
Therefore, Car A traveled at a speed of 55 mph.
To determine how fast Car A traveled, we can use the formula: Speed = Distance/Time.
First, let's introduce some variables:
Let the distance traveled be represented by 'd'.
Let the speed of Car A be represented by 'vA'.
Let the speed of Car B be represented by 'vB'.
Let the time taken by Car A be represented by 'tA' (given as 2.4 hours).
Let the time taken by Car B be represented by 'tB' (given as 4 hours).
We know that Car A traveled the same distance as Car B, so we can equate the distances:
d = d
Next, we can set up two equations based on the information provided:
For Car A: vA = d/tA
For Car B: vB = d/tB
We are also given that Car A traveled 22 mph faster than Car B: vA = vB + 22
We can substitute the values into our equations:
vA = d/tA
vB = d/tB
vA = vB + 22
Since both cars traveled the same distance, we can equate the two expressions for speed:
d/tA = d/tB + 22
Now we can solve for the speed of Car A:
d/tA = d/tB + 22
Dividing both sides of the equation by d, we get:
1/tA = 1/tB + 22/d
Rearranging the equation, we have:
1/tA - 1/tB = 22/d
Now, let's substitute the given values:
1/2.4 - 1/4 = 22/d
Simplifying the equation, we get:
(4 - 2.4) / (2.4 * 4) = 22/d
1.6 / 9.6 = 22/d
0.1667 = 22/d
To isolate 'd', we divide both sides of the equation by 0.1667:
d = 22 / 0.1667
Calculating this value, we find:
d ≈ 132
Now, we can substitute the value of 'd' back into one of the equations to find the speed of Car A:
vA = d / tA
vA = 132 / 2.4
Calculating this value, we find:
vA ≈ 55
Therefore, Car A traveled at approximately 55 mph.