Question

two trains leave a railway station at the same time. the first train travels due west and the second due north. the first train travels 35 km/h faster than the second train. if after two hours, they are 130 km apart, find the average speed of each train.

Answer 1

Using the Pythagorean theorem, the average speed of the second train is found to be 30 km/h and the first train 65 km/h, as they form a right-angled triangle with distances covered as legs.

Step-by-step explanation:

To solve this problem, we can use the Pythagorean theorem because the trains are moving in perpendicular directions (west and north), creating a right-angled triangle after a certain time period. Let's denote the speed of the second train as V km/h and the speed of the first train as V + 35 km/h. After two hours, the second train has traveled a distance of 2V km, and the first train has traveled a distance of 2(V + 35) km.

Since the trains are 130 km apart, we can write:

(2V)² + [2(V + 35)]² = 130²

Now, we simplify and solve the equation:

1. 4V² + 4(V + 35)² = 16900
2. 4V² + 4(V² + 70V + 1225) = 16900
3. 4V² + 4V² + 280V + 4900 = 16900
4. 8V² + 280V + 4900 - 16900 = 0
5. 8V² + 280V - 12000 = 0
6. Divide by 8: V² + 35V - 1500 = 0
7. Solve for V using the quadratic formula, or factorising: (V - 30)(V + 50) = 0
8. V = 30 km/h (since speed cannot be negative, we disregard the -50 result)

Therefore, the average speed of the second train is 30 km/h and the first train is 65 km/h (30 km/h + 35 km/h).