Answer:
The particles meet at the end of 25 seconds of travel. At the end of 25 seconds, the first particle has traveled 675 cm, and the second particle has traveled 325 cm.
Explanation:
Make a table where you keep track of each second, the position of each particle, the cumulative traveled distance of each particle, and the total distance traveled by both particles.
Let the particle that travels 51cm in the 1st second, 49 cm in the 2nd, 47 cm in the 3rd, etc. be called Particle A.
Let the particle that travels 25 cm in the 1st second, 24 cm in the 2nd, 23 cm in the 3rd, etc. be called Particle B.
The particles are at the opposite ends of a 10-m tube. To meat, they need to have traveled a combined 10 m. 10 m = 1000 cm. We write the table until the combined total traveled is 1000 cm.
second Particle A Particle A Particle B Particle B combined
total total total
1 51 51 25 25 76
2 49 100 24 49 149
3 47 147 23 72 219
4 45 192 22 94 286
5 43 235 21 115 350
6 41 276 20 135 411
7 39 315 19 154 469
8 37 352 18 172 524
9 35 387 17 189 576
10 33 420 16 205 625
11 31 451 15 220 671
12 29 480 14 234 714
13 27 507 13 247 754
14 25 532 12 259 791
15 23 555 11 270 825
16 21 576 10 280 856
17 19 595 9 289 884
18 17 612 8 297 909
19 15 627 7 304 931
20 13 640 6 310 950
21 11 651 5 315 966
22 9 660 4 319 979
23 7 667 3 322 989
24 5 672 2 324 996
25 3 675 1 325 1000
The particles meet at the end of 25 seconds of travel. At the end of 25 seconds, Particle A has traveled 675 cm, and particle B has traveled 325 cm.