Question

A trucks relation to a car is -60. The car and truck move in the same direction. The car moves five times as fast for 8 seconds. Where is the truck in relation to the car? What operations would you use to solve this and why?

Answer 1

Explanation:

We are not given units for distance or speed. The only units we're given are for time (seconds). Let the car's speed be represented by "v".

When the truck is moving 5 times as fast as the car, its relative speed is ...

  5v -v = 4v

For some time (t) at the higher speed, it will move a distance farther than the car moves. That distance is the product of the relative speed and the corresponding time period: 4vt. Since the speeds are in the same direction, this additional distance is added to the initial relative location of the truck, -60. The new position of the truck relative to the car is ...

  -60 +4vt = -60 +4v(8 seconds)

  -60 + 32v . . . . . new position of the truck in relation to the car

(This only makes sense if the units of v are the same distance units as -60 and time units of seconds.)

__

At least, operations of multiplication and addition are needed. Depending on the units of speed and distance, units conversion may also be required.