distance problem

2.  Distance Problems are solved
using the concept that the
distance equals the product of
rate and time: d= rt. Drawing the
diagram will very often help you
to write the needed equation.

3.  Carol and John leave the same
place and travel on the same road.
Carol walks at a rate of two miles
per hour. Carol left five hours
earlier than Jan, but Jan bikes at a
rate of 6 miles per hour. When will
Jan catch up?

4. Draw a diagram like the one right.
Carol’s head start:
d=rt=5 ∙ 2= 10.
If t= time for Jan to catch carol,
Jan’s distance during that time is
d=rt = 6t and Carol’s is 2t.

5.  The equation is:
10+2t= 6t 10
= 4t
= 2.5 hours.

6.  Two trucks leave the rest stop at the
same time. One heads due to east; the
other due north and travels twice as
fast as the first truck. The truck lost
radio contact when they are 47 miles
apart. How far has each truck travelled
when they lost contact?

7.  Draw a top diagram. Since both
trucks travel at the same time and
north truck is travelling twice as
fast as the first truck, its distance
is twice as long. If x= distance of
the east truck, our diagram now
becomes the right angle in the
bottom diagram.

8. From the Pythagorean Theorem we
have:
(2x) 2 t x2= 472 4x2+ x2
= 441.8 x ≈ 21
The east truck travelled 21 miles and
the north truck travelled 42 miles.

9. 1.Matilda and Nancy are 60miles apart, bicycling toward each other
on the same road. Matilda rides 12 miles per hour while Nancy
rides eight miles per hour. In how many hours will they meet?
2.Two cars start together and travel in the same direction. One car
travels twice as fast as the other. After five hours they are 275
kilometres apart. How fast is each car travelling?
3. Two cars leave a parking lot together at the same time. One car
travels south at 55 mph and the other cars travels 45mph. How
long will it take until the cars are 150 miles apart?
4. A cheetah spots a gazelle 132 miles away. The cheetah starts
toward the gazelle at a speed of 18 meters per second. At the
same instant, the gazelle starts moving away from the cheetah at
11 meters per second. How long will it take to the cheetah to get
dinner?
5 Two trucks leave the same rest stop at the same time travelling
at the same speed. One heads south and the other travel west.
When the two trucks lost CB contact, they are 53 miles apart.
How far has each truck travelled?

11.  Geometry is simple to
understand. Always start with
the basic shape properties
improving theorems and
axioms.

12.  Understand the problem.
 Be open-minded
 Memorized the theorems.
 Postulate axioms.
 Translate theoretical problems to practical
problems to better understand.
 Teach geometry through practical methods.
Create fun yet educating experience
environment for the students/learners. Solve
as many problems as possible to practice.

13. Suppose a water tank in the
shape of a right circular
cylinder is thirty feet long
and eighty feet in diameter.
How much sheet metals
was used in its
construction?

14.  What is asked? Surface area
 Draw/illustrate side view of the cylindrical
tank showing the radius r an exploded view
of the tank showing the three separate
surfaces whose areas are needed to find.
 Total Surface Area 2x (pi) r2 + 2(pi) rh (the
two ends, plus the cylinder) = 2 (pi) (42) + 2
(pi) (4) (30)
 = 2((pi) x 16) + (240(pi)
 = 32(pi) + 240 (pi)
 =272pi

15.  Since the original dimensions
were the surface area given in
terms of is 272 (pi) square
feet, then the area feet, must
be in terms of square feet:

16.  A circular swimming pool with a diameter of 28 feet has a deck
of uniform width built around it. If the area of the deck is 60(pi)
square feet, find its width.
 A pool is surrounded by a deck. The pool has radius 14 meters
and the deck has 15 meters.
 A piece of 16 gauge copper wire is 42 cm long is bent into the
shape of a rectangle whose width is twice its length. Find the
dimensions of the rectangle.
 If one of the side of a square is doubled in length and the
adjacent side is decreased by two centimetres, the area of the
resulting triangle is 96 square cm larger than that of original
square. Find the dimension of the rectangle.
 If the height of the triangle is five inches less than the length of
its base, and if the area of the triangle is 52 square inches, find
the base and the height.