diff --git a/library/std/src/sys/hermit/time.rs b/library/std/src/sys/hermit/time.rs
index 32ddc4346eefd..5440d85df4adf 100644
--- a/library/std/src/sys/hermit/time.rs
+++ b/library/std/src/sys/hermit/time.rs
@@ -40,11 +40,7 @@ impl Timespec {
     }
 
     fn checked_add_duration(&self, other: &Duration) -> Option<Timespec> {
-        let mut secs = other
-            .as_secs()
-            .try_into() // <- target type would be `libc::time_t`
-            .ok()
-            .and_then(|secs| self.t.tv_sec.checked_add(secs))?;
+        let mut secs = self.tv_sec.checked_add_unsigned(other.as_secs())?;
 
         // Nano calculations can't overflow because nanos are <1B which fit
         // in a u32.
@@ -57,11 +53,7 @@ impl Timespec {
     }
 
     fn checked_sub_duration(&self, other: &Duration) -> Option<Timespec> {
-        let mut secs = other
-            .as_secs()
-            .try_into() // <- target type would be `libc::time_t`
-            .ok()
-            .and_then(|secs| self.t.tv_sec.checked_sub(secs))?;
+        let mut secs = self.tv_sec.checked_sub_unsigned(other.as_secs())?;
 
         // Similar to above, nanos can't overflow.
         let mut nsec = self.t.tv_nsec as i32 - other.subsec_nanos() as i32;
diff --git a/library/std/src/sys/solid/time.rs b/library/std/src/sys/solid/time.rs
index ce31cb45a69a1..f83f1644fe854 100644
--- a/library/std/src/sys/solid/time.rs
+++ b/library/std/src/sys/solid/time.rs
@@ -47,10 +47,10 @@ impl SystemTime {
     }
 
     pub fn checked_add_duration(&self, other: &Duration) -> Option<SystemTime> {
-        Some(SystemTime(self.0.checked_add(other.as_secs().try_into().ok()?)?))
+        Some(SystemTime(self.0.checked_add_unsigned(other.as_secs())?))
     }
 
     pub fn checked_sub_duration(&self, other: &Duration) -> Option<SystemTime> {
-        Some(SystemTime(self.0.checked_sub(other.as_secs().try_into().ok()?)?))
+        Some(SystemTime(self.0.checked_sub_unsigned(other.as_secs())?))
     }
 }
diff --git a/library/std/src/sys/unix/time.rs b/library/std/src/sys/unix/time.rs
index a61d926ca8b3a..a9fbc7ab108a4 100644
--- a/library/std/src/sys/unix/time.rs
+++ b/library/std/src/sys/unix/time.rs
@@ -113,11 +113,7 @@ impl Timespec {
     }
 
     pub fn checked_add_duration(&self, other: &Duration) -> Option<Timespec> {
-        let mut secs = other
-            .as_secs()
-            .try_into() // <- target type would be `i64`
-            .ok()
-            .and_then(|secs| self.tv_sec.checked_add(secs))?;
+        let mut secs = self.tv_sec.checked_add_unsigned(other.as_secs())?;
 
         // Nano calculations can't overflow because nanos are <1B which fit
         // in a u32.
@@ -126,15 +122,11 @@ impl Timespec {
             nsec -= NSEC_PER_SEC as u32;
             secs = secs.checked_add(1)?;
         }
-        Some(Timespec::new(secs, nsec as i64))
+        Some(Timespec::new(secs, nsec.into()))
     }
 
     pub fn checked_sub_duration(&self, other: &Duration) -> Option<Timespec> {
-        let mut secs = other
-            .as_secs()
-            .try_into() // <- target type would be `i64`
-            .ok()
-            .and_then(|secs| self.tv_sec.checked_sub(secs))?;
+        let mut secs = self.tv_sec.checked_sub_unsigned(other.as_secs())?;
 
         // Similar to above, nanos can't overflow.
         let mut nsec = self.tv_nsec.0 as i32 - other.subsec_nanos() as i32;
@@ -142,7 +134,7 @@ impl Timespec {
             nsec += NSEC_PER_SEC as i32;
             secs = secs.checked_sub(1)?;
         }
-        Some(Timespec::new(secs, nsec as i64))
+        Some(Timespec::new(secs, nsec.into()))
     }
 
     #[allow(dead_code)]
diff --git a/library/std/src/time/tests.rs b/library/std/src/time/tests.rs
index 2e64ae59aff24..6ed84806e6d37 100644
--- a/library/std/src/time/tests.rs
+++ b/library/std/src/time/tests.rs
@@ -1,4 +1,5 @@
 use super::{Duration, Instant, SystemTime, UNIX_EPOCH};
+use core::fmt::Debug;
 #[cfg(not(target_arch = "wasm32"))]
 use test::{black_box, Bencher};
 
@@ -201,6 +202,32 @@ fn since_epoch() {
     assert!(a < hundred_twenty_years);
 }
 
+#[test]
+fn big_math() {
+    // Check that the same result occurs when adding/subtracting each duration one at a time as when
+    // adding/subtracting them all at once.
+    #[track_caller]
+    fn check<T: Eq + Copy + Debug>(start: Option<T>, op: impl Fn(&T, Duration) -> Option<T>) {
+        const DURATIONS: [Duration; 2] =
+            [Duration::from_secs(i64::MAX as _), Duration::from_secs(50)];
+        if let Some(start) = start {
+            assert_eq!(
+                op(&start, DURATIONS.into_iter().sum()),
+                DURATIONS.into_iter().try_fold(start, |t, d| op(&t, d))
+            )
+        }
+    }
+
+    check(SystemTime::UNIX_EPOCH.checked_sub(Duration::from_secs(100)), SystemTime::checked_add);
+    check(SystemTime::UNIX_EPOCH.checked_add(Duration::from_secs(100)), SystemTime::checked_sub);
+
+    let instant = Instant::now();
+    check(instant.checked_sub(Duration::from_secs(100)), Instant::checked_add);
+    check(instant.checked_sub(Duration::from_secs(i64::MAX as _)), Instant::checked_add);
+    check(instant.checked_add(Duration::from_secs(100)), Instant::checked_sub);
+    check(instant.checked_add(Duration::from_secs(i64::MAX as _)), Instant::checked_sub);
+}
+
 macro_rules! bench_instant_threaded {
     ($bench_name:ident, $thread_count:expr) => {
         #[bench]