Question

Alice and Bob race two toy trains around a circular track. The trains move in the same direction and they meet every 120 seconds. If Alice's and Bob's toy trains move in opposite directions, at constant rates, they meet every 30 seconds. If the track is 1800 m long, what is the speed of each toy train?

Answer 1

When Alice and Bob's toy trains move in the same direction, their relative speed is the sum of their individual speeds. When they move in opposite directions, their relative speed is the difference between their individual speeds. By solving simultaneous equations, we find that Alice's toy train has a speed of 75 m/s and Bob's toy train has a speed of 60 m/s.

Step-by-step explanation:

Let's assume the speed of Alice's toy train is x m/s and the speed of Bob's toy train is y m/s.

When the trains move in the same direction, they meet every 120 seconds. Since they meet once every 30 seconds when moving in opposite directions, their relative speed is the sum of their individual speeds. So, when they move in the same direction, their relative speed will be x + y and when they move in opposite directions, their relative speed will be x - y.

When they move in the same direction, the distance covered by Alice's toy train in 120 seconds will be equal to the distance covered by Bob's toy train in 120 seconds, which is equal to the length of the circular track (1800 m). So, the equation can be written as:

1. x × 120 = y × 120 = 1800

Simplifying the equation, we get:

1. x + y = 1800/120 = 15

Similarly, when they move in opposite directions, the distance covered by Alice's toy train in 30 seconds will be equal to the distance covered by Bob's toy train in 30 seconds:

1. x × 30 = y × 30 = 1800

Simplifying the equation, we get:

1. x - y = 1800/30 = 60

Solving the equations simultaneously, we find that x = 75 m/s and y = -60 m/s. Since speed is always positive, we consider the magnitude of the velocity. Therefore, the speed of Alice's toy train is 75 m/s and the speed of Bob's toy train is 60 m/s.

Answer 2

Step-by-step explanation:

Given that Alice and Bob race two toy trains around a circular track. The trains move in the same direction and they meet every 120 seconds. If Alice's and Bob's toy trains move in opposite directions, at constant rates, they meet every 30 seconds

Circular track is 1800 m.

Let speed be x and y respectively

When in same direction relative speed = x-y and when in opposite directions =x+y

30(x+y) = 1800

x+y= 60

120(x-y) = 1800

x-y = 15

Solving x = 37.5 m/hr and y = 12.5 per hour.