diff --git a/Library/Homebrew/downloadable.rb b/Library/Homebrew/downloadable.rb
index 9d732e237a..c352191c8e 100644
--- a/Library/Homebrew/downloadable.rb
+++ b/Library/Homebrew/downloadable.rb
@@ -132,6 +132,26 @@ module Downloadable
     EOS
   end
 
+  sig { returns(Integer) }
+  def hash
+    [self.class, cached_download].hash
+  end
+
+  sig { params(other: Object).returns(T::Boolean) }
+  def eql?(other)
+    return false if self.class != other.class
+
+    other = T.cast(other, Downloadable)
+    cached_download == other.cached_download
+  end
+
+  sig { returns(String) }
+  def to_s
+    short_cached_download = cached_download.to_s
+                                           .delete_prefix("#{HOMEBREW_CACHE}/downloads/")
+    "#<#{self.class}: #{short_cached_download}>"
+  end
+
   private
 
   sig { overridable.returns(String) }
diff --git a/Library/Homebrew/test/cmd/fetch_spec.rb b/Library/Homebrew/test/cmd/fetch_spec.rb
index f63c977f9b..b8a8241ca0 100644
--- a/Library/Homebrew/test/cmd/fetch_spec.rb
+++ b/Library/Homebrew/test/cmd/fetch_spec.rb
@@ -26,14 +26,4 @@ RSpec.describe Homebrew::Cmd::FetchCmd do
     expect(HOMEBREW_CACHE/"testball2--0.1.tbz").to be_a_symlink
     expect(HOMEBREW_CACHE/"testball2--0.1.tbz").to exist
   end
-
-  it "errors when concurrently downloading to the same destination", :integration_test do
-    # This test will fail if the fetch is not performed concurrently.
-    # N.B. this test relies on how we set up test formulae, see the `integration_test` shared context.
-    setup_test_formula "testball1"
-    setup_test_formula "testball3"
-
-    expect { brew "fetch", "testball1", "testball3", "HOMEBREW_DOWNLOAD_CONCURRENCY" => "2" }.to be_a_failure
-      .and output(/Error:.*process has already locked/).to_stderr
-  end
 end