Question

Train A has a speed 35 miles per hour greater than that of train B. If train A travels 320 miles in the same times train B travels 250 miles, what are the speeds of the two trains ?

Answer 1

The problem involves setting up equations based on the relationship between speed, distance, and time for two trains. Train B's speed is found to be 50 mph while Train A's speed is 85 mph.

Step-by-step explanation:

Finding the Speeds of Two Trains

To solve the problem, we should first acknowledge that the time taken by Train A and Train B is the same since they travel simultaneously. Let's denote the speed of Train B as v mph. According to the question, Train A has a speed that is 35 mph greater than Train B, so the speed of Train A will be (v + 35) mph.

Using the formula for speed, which is speed = distance/time, we have the equations:

• Speed of Train A: (v + 35) = 320/t
• Speed of Train B: v = 250/t

To find the value of v, we can set up the equation (v + 35) = 320/t and solve for t from the second equation:

• v = 250/t → t = 250/v

Substituting t into the first equation:

• (v + 35) = 320/(250/v)

After solving the equation, we find v = 50 mph for Train B and v + 35 = 85 mph for Train A.