He didn't. The position given in that message from Rostron to Haddock on April 15th was Carpathia's position, not Olympic's. Rostron was simply informing Haddock where his ship, Carpathia, was at a specific point in time, and more importantly, where he was headed. Unlike others here on this forum who somehow knows all about the conversation that took place between Rostron, Lightoller and Boxhall, I only pointed out an observation that produces a very interesting and very suspicious coincidence. Nobody can deny that Carpathia's position given by Rostron in that message to Haddock is precisely 3h 27m behind GMT; the exact same time difference we find in the message he sent to Haddock just 45 minutes later when he gave the time Titanic foundered in ship's time and GMT.Haddock sent this telegram to Rostron. But why should Rostron do any calculation about mean solar time of Haddock's position?
It is all too easy to assume what some people knew or didn't know. But I do not for a moment believe that Rostron would ask what the time difference was between Titanic time and NY time. As Jim Currie points out many times here, the only time that mattered to ship's officers is ship's time, by which they stood watch and ate and slept, and Greenwich mean time by which they used to navigate. Rostron was clearly interested in what GMT was when it was 2:20am ship's time on Titanic. Mean solar time at the Ambrose light vessel was irrelevant, so too was mean solar time for New York city. Sen. Burton's remark was not only a bit strange, but also incorrect. Mean solar time for NY was and still is 4h 56m behind GMT, not 4h 57m as Burton announced. Mean solar time at the Ambrose channel light vessel, the official arrival/departure point for ships going in and out NY harbor, was 4h 55m behind GMT and appears in Reed's table. But Sen. Smith asked what the time was in NY when Titanic foundered so he could put it in the record. Notice that he told Pitman that he was given ship's time and Greenwich time which he just happen to get from Lightoller. He also answered his own question after Pitman told him to take 5 hours off Greenwich time, but Smith wanted Pitman to work it out and gave Pitman the foundering time in GMT that Lightoller gave him just a few minutes earlier after Pitman asked him "Give me the Greenwich time, please?" What's funny is that Pitman got 11:47 by subtracting 5 hours from 5:47, something Sen. Burton immediately noted and Sen. Smith corrected to 12:47. The exchanges between the three, Pitman, Smith and Burton, is almost comical.
I have a suspicion as to how that 3h 27m difference came about, but I'll save that for another post. Just note that it never surfaced at the British inquiry which decided on something totally different altogether.