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.