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?

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