The movement of a truck is described by the equation x1 = -270 + 12t, and movement on the side of the same highway – by the equations x2 = -1.5t. Determine the place and time of the meeting.
x1 = -270 + 12 * t – the equation of motion of the truck;
x2 = -1.5 * t – equation of movement of another car on the same highway.
It is required to determine t (seconds) – meeting time and x (meter) – meeting point of two cars.
At the meeting point of the cars, their coordinates will be the same. Then:
x1 = x2;
-270 + 12 * t = -1.5 * t;
12 * t + 1.5 * t = 270;
t * (12 + 1.5) = 270;
t * 13.5 = 270;
t = 270 / 13.5 = 20 seconds.
Then the meeting coordinate will be:
x = -1.5 * t = -1.5 * 20 = -30 meters.
Answer: the cars will meet in 20 seconds at the point x = -30 meters.
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