updating existing data on google spreadsheet using a form?

I believe you can found everything you want here.
It's a form url, when you answer this form you'll have the url of the spreadsheet where the data are stored. One of the information stored is the url to modify your response, if you follow the link it will open the form again and update the spreadsheet in consequence. the code to do this trick is in the second sheet of the spreadsheet.
It's a google apps script code that need to be associated within the form and triggered with an onFormSubmit trigger.

Maybe I missed something in your question but I don't really understand Harold's answer... Here is a code that does strictly what you asked for, it counts the total cumulative value of 4 numbers entered in a form and shows it on a Spreadsheet.

I called the 4 questions "race number 1", "race number 2" ... and the result comes on row 2 so you can setup headers.

I striped out any non numeric character so you can type responses more freely, only numbers will be retained.

form here and SS here (raw results in sheet1 and count in Sheet2)

script goes in spreadsheet and is triggered by an onFormSubmit trigger.

function onFormSubmit(e) {
  var sh = SpreadsheetApp.getActiveSpreadsheet().getSheetByName('Sheet2');
  var responses = []
  responses[0] = Number(e.namedValues['race number 1'].toString().replace(/\D/g,''));
  responses[1] = Number(e.namedValues['race number 2'].toString().replace(/\D/g,''));
  responses[2] = Number(e.namedValues['race number 3'].toString().replace(/\D/g,''));
  responses[3] = Number(e.namedValues['race number 4'].toString().replace(/\D/g,''));
  var totals = sh.getRange(2,1,1,responses.length).getValues();
  for(var n in responses){
    totals[0][n]+=responses[n];
  }
  sh.getRange(2,1,1,responses.length).setValues(totals);
}

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edit : I changed the code to allow you to change easily the number of responses... range will update automatically.

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EDIT 2 : a version that accepts empty responses using an "if" condition on result:

function onFormSubmit(e) {
  var sh = SpreadsheetApp.getActiveSpreadsheet().getSheetByName('Sheet2');
  var responses = []
  responses[0] = Number((e.namedValues['race number 1']==null ? 0 :e.namedValues['race number 1']).toString().replace(/\D/g,''));
  responses[1] = Number((e.namedValues['race number 2']==null ? 0 :e.namedValues['race number 2']).toString().replace(/\D/g,''));
  responses[2] = Number((e.namedValues['race number 3']==null ? 0 :e.namedValues['race number 3']).toString().replace(/\D/g,''));
  responses[3] = Number((e.namedValues['race number 4']==null ? 0 :e.namedValues['race number 4']).toString().replace(/\D/g,''));
  var totals = sh.getRange(2,1,1,responses.length).getValues();
  for(var n in responses){
    totals[0][n]+=responses[n];
  }
  sh.getRange(2,1,1,responses.length).setValues(totals);
}