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.

Question

How fast did Car A travel?

(The formula R⋅T=D , where R is the rate of speed, T is the time, and D is the distance can be used.)

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mph

Answer 1

Let the speed of Car B be \( R \) mph. According to the problem, Car A travels 22 mph faster than Car B, so the speed of Car A would be \( R + 22 \) mph.

Given that both cars traveled the same distance \( D \), we can write the equations for the distances traveled by both cars using the formula \( D = R \cdot T \):

1. For Car A:
   \[ D = (R + 22) \cdot 2.4 \]

2. For Car B:
   \[ D = R \cdot 4 \]

Since the distances are equal, we can set the two equations equal to each other:

\[ (R + 22) \cdot 2.4 = R \cdot 4 \]

Now we can solve for \( R \):

Expanding the left side:

\[ 2.4R + 52.8 = 4R \]

Rearranging the equation to isolate \( R \):

\[ 52.8 = 4R - 2.4R \] \[ 52.8 = 1.6R \]

Now, divide both sides by 1.6 to solve for \( R \):

\[ R = \frac{52.8}{1.6} = 33 \]

So, the speed of Car B is 33 mph. Now we can find the speed of Car A:

\[ R + 22 = 33 + 22 = 55 \]

Thus, Car A traveled at a speed of 55 mph.