319.[1] The unchanging velocity is diminished by the first term (of the velocities in series in arithmetical progression), and is (then) divided by the half of the common difference. On adding one (to the resulting quantity), the (required) time (of meeting) is arrive at. (Where two persons travel in opposite directions, each with a definite velocity), twice (the average distance to be covered by either of them) is the (whole) way (to be travelled). This when divided by the sum of their velocities gives rise to the time of (their) meeting.
An example in illustration thereof.
320. A certain person goes with a velocity of 3 in the beginning increased (regularly) by 8 as the (successive) common difference. The steady unchanging velocity (of another person) is 21. What may be the time of their meeting (again, if they start from the same place at the same time, and move in the same direction)?
An example in illustration of the latter half of the rule given in the steps above
321-321. One man travels at the rate of 6 yōjanas and another at the rate of 3 yōjanas. The (average) distance to be covered by either of them moving in opposite directions is 108 yōjanas. O arithmetician, tell me quickly what the time of their meeting together is.
The rule for arriving at the time and distance of meeting together, (when two persons start from the same place at the same time and travel) with (varying) velocities in arithmetical progression.
322.[2] The difference between the two first terms divided by the difference between the two common differences, when multiplied by two and increased by one, gives rise to the time of coming together on the way by the two persons travelling simultaneously (with two series of velocities varying in arithmetical progression).
319.^ Algebraically, , where v is the unchanging velocity, and t the time.
322.^ Algebraically, .
