L MAY ACADEMY
Address: Lot 18, Dinh Cong Urban Area, Hoang Mai, Hanoi
TOPIC 1
PROBLEM WITH TREE
MAY ACADEMY
Week 4
KNOWLEDGE
There are 3 scenarios for problems of this nature.
a) If both ends of the road are planted with trees
number of trees = number of intervals + 1
number of intervals = number of trees − 1
b) If one end of the road is planted with a tree,
number of trees = number of intervals
c) If both ends of the road have no trees,
number of trees = number of intervals − 1
number of intervals = number of trees + 1
EXAMPLE
EXAMPLE 1. Trees are to be planted along a road that is 40 m long. The distance between every two trees is
8 m. How many trees can be planted if both ends of the road are to be planted with trees?
EXAMPLE 2. Lamp posts are to be placed along a road. The distance between every two lamp posts is 10 m.
How long is the road if a total of 16 lamp posts are to be placed along the road, including both ends?
EXAMPLE 3. A road, 120 m long, is planted with 16 trees at regular intervals. How far is one tree from another
if both ends of the road are also planted with trees?
EXAMPLE 4. Melissa’s mum embroiders 5 flowers on each side of a handkerchief. There is one flower at each
corner, how many flowers are embroidered on the handkerchief altogether?
EXAMPLE 5. A grandfather’s clock takes 12 seconds to chime 4 times at 4 o’clock. How long does it take to chime
7 times?
EXERCISE
EXERCISE 1. Joe puts 5 matchsticks on a table. Each matchstick is 10 cm away from another. How far is the
fifth matchstick away from the first one?
EXERCISE 2. A sailor ties 7 knots on a rope at regular intervals The distance from the first knot to the seventh
one is 18 m long. What is the distance between every two knots?
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Duc Tran Thien –
+84.902468000
L MAY ACADEMY
Address: Lot 18, Dinh Cong Urban Area, Hoang Mai, Hanoi
EXERCISE 3. A road, 500 m long, is to be planted with trees at an interval of 5 m. How many trees can be
planted if trees are planted at both ends of the road as well?
EXERCISE 4. It takes John 8 minutes to saw a piece of log into 3 equal lengths. How long does ít take for him to
saw the same piece of log into 9 equal lengths?
EXERCISE 5. David uses some coins to form a triangle. There is a coin at every corner. How many coins does he
use if there are 6 coins on each side of the triangle?
EXERCISE 6. trees are planted at regular intervals from the begining of a road to the end of it. The distance
between every two trees is 5 m. How long is the road?
EXERCISE 7. 16 lamp posts are placed at regular intervals along a road 300 m long. If lamp posts are placed at
both ends of the road as well, how far is one lamp post from another?
EXERCISE 8. 21 trees are to be planted along a road 800 m long at regular intervals. If both ends of the road are
planted with trees as well, how far is one tree from another?
EXERCISE 9. Melvin stays on the 5th floor of an apartment. Nick stays on the next floor. The staircases leading
to Melvin’s house have 80 steps. How many steps have the staircases leading to Nick’s house?
EXERCISE 10. My grandfather’s clock takes 6 seconds to chime 3 times at 3 o’clock. How long does ít take to
chime 6 times at 6 o’clock?
EXERCISE 11. It takes Uncle Sam 50 seconds to cycle from the first lamp post to the eleventh lamp post. How
many lamp posts will he cycle past after 80 seconds?
EXERCISE 12. Each side of a fotball field is planted with 16 flags. There is one flag at each corner. How many
flags are planted altogether in the fotball field?
EXERCISE 13. Pots of flowers are used to decorate the edges of a square garden. The distance between every two
pots of flowers is 3 m. The side of the square garden is 24 m. How many pots of flowers are needed?
EXERCISE 14. Stella tied 6 knots on a piece of ribbon. The length between the second and fifth knots was 60 cm.
What was the length between the first and sixth knots?
EXERCISE 15. A Greyhound coach leaves the station every 10 minutes. How many coaches will leave the station
in 60 minutes?
EXERCISE 16. It takes Professor Sullivan 11 minutes to stroll past the twelfth lamp post along a quiet road. How
many lamp posts will he stroll past after 30 minutes.
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Duc Tran Thien –
+84.902468000