car a leaves phoenix heading north at a constant speed of 40mph car b leaves two hours later and follows car a at a constant speed of 54 mph how many hours does it take car b to catch up to car a? algebra

in the first 2 hours, A moved 80 miles.

B is going 14 mi/hr faster than A.

So, it takes 80/14 hours to catch up.

To determine how many hours it takes for car B to catch up to car A, we need to set up an equation based on their relative positions and speeds.

Let's say the time it takes for car B to catch up to car A is "t" hours after car B starts. Since car B leaves two hours later, car A would have already been driving for 2 + t hours.

Now, we can calculate the distance each car has traveled using the formula: Distance = Speed × Time.

For car A, the distance it travels is 40 × (2 + t) miles.
For car B, the distance it travels is 54t miles.

When car B catches up to car A, they will have traveled the same distance. So we can set up the equation:

40 × (2 + t) = 54t

Now, we can solve this equation for t.

First, distribute the 40 to the terms inside the parentheses:

80 + 40t = 54t

Next, subtract 40t from both sides to isolate the variable:

80 = 14t

Finally, divide both sides by 14 to solve for t:

t = 80 ÷ 14

Using a calculator, we can determine that t is approximately 5.71 hours.

Therefore, it takes car B approximately 5.71 hours to catch up to car A.