Question

The truck and the car are moving at constant speeds. Write an expression, in terms of t, for the position of the taxi so that both statements below are true. 1. It is never in the same position as the truck. 2. It will be in the same position as the car when t=8.

Answer 1

The expression for the position of the taxi in terms of time can be written as x = v2t, where v2 is the velocity of the car and t is the time.

Step-by-step explanation:

To write an expression for the position of the taxi, we can use the equation: position = initial position + velocity × time. Let's assume that the initial position of the taxi is x, and the velocity of the car and the truck are v1 and v2, respectively. Given that the taxi is never in the same position as the truck, we can write the expression as: x = v1t. Now, we need to find the position of the car when t = 8. We know that the car's position at t = 8 should be the same as the taxi's position at that time. So, we can write another expression: v1(8) = v2(8). Solving for v1, we get: v1 = v2. Substituting this into the expression for the position of the taxi, we get: x = v2t.

Answer 2

The expression for the position of the taxi in terms of t is x * t + 320 km.

Step-by-step explanation:

To write an expression, in terms of t, for the position of the taxi, we need to consider the movements of the truck, car, and taxi.

Let's assume that the truck is moving at a constant speed of 60 km/h to the west, and the car is moving at a constant speed of 40 km/h to the east.

When t = 8, the car will be 8 * 40 = 320 km east of its initial position.

To ensure that the taxi is never in the same position as the truck, we can assume that the taxi is also moving at a constant speed, but in the opposite direction of the truck.

Let's say the taxi is moving at a speed of x km/h to the east.

Therefore, the expression for the position of the taxi in terms of t is: x * t + 320 km