SME
Grade 12 Science · Problem type
A dike cutting the layers: cross-cutting
Use this for “A 105-million-year-old dike cuts the sandstone but not the shale above it. How old can the shale’s fossils be?”
Diagram
The shale is older than 92 and younger than 105 million years.
This is an example. Type your own values to start a new problem.
a
Age of the upper ash bed
example · million years
i
Age of the dike
example · million years
b
Age of the lower ash bed
example · million years
w
Width of the shale’s bracket
worked out (not typed) · million years
d
Narrowed by the dike
worked out (not typed) · million years
Formulas
w
=
i
−
a
13 = 105 − 92
d
=
b
−
i
15 = 120 − 105
Assumptions
•
Cross-cutting: a dike is younger than every layer it cuts, and older than the layers laid down across its eroded top.
•
Superposition: a layer is younger than the layers under it and older than those on top.
•
The dike and the ash beds cooled from magma, so they can be dated; the shale cannot, so its age is bracketed.
Step-by-step
WE KNOW
a = 92 million years, i = 105 million years, b = 120 million years
FIND
width of the shale’s bracket (w), narrowed by the dike (d)
Step 1 · Find width of the shale’s bracket (w)
Use w = i − a
The
shale
lies
above
the
dike’s
top,
so
it
is
younger
than
the
dike
and
older
than
the
upper
ash:
from
a
to
i
.
w
=
105
−
92
w
=
13
million
years
Step 2 · Find narrowed by the dike (d)
Use d = b − i
Without
the
dike
the
shale
could
be
as
old
as
the
lower
ash
bed;
the
dike
takes
b
−
i
off
the
bracket.
d
=
120
−
105
d
=
15
million
years
Check
Put the numbers back in. Both sides should match.
13 = 105 − 92 ✓
15 = 120 − 105 ✓
Topic check
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