Math Problem

Let's say I have an array of 8 objects. Each object represents a task which can be completed multiple times. 
In this case, the goal is to complete each task as many times as possible, until the allotted time per task is up
and I must move on to the next task. Let's also say that I have a total of ten minutes (600 seconds) to spend on
all tasks combined. Using javascript, how can I assign a random number of seconds (no less than 45, assuming each
task takes a minimum of 45 seconds to complete once) to each object so that the combined total of seconds adds up
to exactly 600? In other words, how do I split 600 into 8 random numbers where each random number is >= 45, and
all combined numbers add to 600?

Q. do the allotted task times need to be evenly divisible by 45?
Q. if max budget time is 660, and there are 8 tasks that require a minimum of 45 seconds, then the minimum allotment is 360 seconds?
Q. if that's true, then the difference to be randomly divided is 240 seconds -- since not all tasks can be run twice in that case, is there another decision about allocating time you'd want to make?

Q. do the allotted task times need to be evenly divisible by 45?
No, 45 is just the smallest possible value
Q. if max budget time is 660, and there are 8 tasks that require a minimum of 45 seconds, then the minimum allotment is 360 seconds?
Max budget time is 600, but yeah that's correct
Q. if that's true, then the difference to be randomly divided is 240 seconds -- since not all tasks can be run twice in that case, is there another decision about allocating time you'd want to make?
Nope, the idea is that you might be able to complete a task from 1 to N times, where N does not exceed 240

Q. do the allotted task times need to be evenly divisible by 45?
Q. if max budget time is 660, and there are 8 tasks that require a minimum of 45 seconds, then the minimum allotment is 360 seconds?
Q. if that's true, then the difference to be randomly divided is 240 seconds -- since not all tasks can be run twice in that case, is there another decision about allocating time you'd want to make?

I think start with an array of runtimes.
If we start with "every task runs for 45 seconds" then we have a maximum of 13 run times we can allocate, with 15 seconds leftover.
Q. do the tasks have maximum run times? or max time after which they can be aborted?
You could then either allocated runtimes by task max time (a task needs 120 seconds to complete, e.g.) and allocate enough runtimes to that task before allocating to the next one, etc.

Work in progress - pay no attention

var tasks = Array(8).fill(0).map(function(v, i) {
  return { name: 'task_' + i, runtime: 45 };
});

var budget = 600;
var remainder = budget - Math.ceil(budget / 45) - (tasks.length * 45);
console.log(remainder);
function getRandomIntInclusive(min, max) {
  min = Math.ceil(Math.random() * (max - min + 1)) + 1; //The maximum is inclusive and the minimum is inclusive
  
  return min;
}

tasks.forEach(task => {
  var time = getRandomIntInclusive(task.runtime, remainder);
  
  console.log(time, remainder);
  
  task.runtime += time;
  remainder -= time;
  
  if (remainder <= 0) {
    remainder = 0;
  }
});

console.log(tasks);

var total = tasks.reduce(function(total, task) {
  return total + task.runtime;
}, 0);

console.dir(total);

5 Sept 2019, I've updated with a possible solution and postscript here => https://gist.github.com/dfkaye/29e28a2a1005704e59467417432203b3