Solving Math textbook exercises 5 Lessons: Practice
1. Solve problem 1 page 171 Math textbook 5
a) Find the speed of a car that travels \(120km\) in \(2\) hours \(30\) minutes.
b) Binh rides a bicycle at a speed of \(15km\)/hour from his house to the bus station in half an hour. How many kilometers is Binh’s house from the bus station?
c) A person walks at a speed of \(5km\)/hr and covers a distance \(6km\). How long has the person been gone?
Solution method
– Convert given time measurements to hours
Apply the following formulas:
\(v = s : t\)
\(s = v × t\)
\(t = s : v\)
(Where \(s\) is distance, \(v\) is speed and \(t\) is time)
Solution guide
Convert: \(2\) hours \(30\) minutes = \(2,5\) hours
Half an hour = \(0.5\) hour
a) The speed of the car is:
\(120 : 2.5 = 48 \,(km\)/hour\()\)
b) The distance from Binh’s house to the bus station is:
\(15 \times 0.5 = 7.5 \, (km)\)
c) The time the person walked is:
\(6 : 5 = 1,2\) (hour)
Answer:
a) \(48km\)/hour
b) \(7.5km\)
c) \(1,2\) hours
2. Solve problem 2 page 171 Math textbook 5
A car and a motorbike start at the same time from A to B. Distance AB is \(90\text{km}\). How long before the car arrives at B, given that the car’s travel time is \(1.5\) hours and the car’s speed is \(2\) times the motorbike’s speed?
Solution method
Step 1: Find the speed of the car given the distance is \(90\text{km}\), the time is \(1.5\) hours
Step 2: Calculate the speed of the motorbike, if the speed of the car is twice the speed of the motorbike
Step 3: Calculate the time taken by the motorbike to travel the distance AB
Step 4: Calculate the time the car arrives in front of the motorbike
Solution guide
The speed of the car is:
\(90 : 1.5 = 60\) (km/hr)
The speed of the motorcycle is:
\(60 : 2 = 30\) (km/hr)
Time taken by car to travel distance AB is:
\(90 : 30 = 3\) (hour)
Then the car arrives B before the motorbike a time is:
\(3 – 1.5 = 1.5\) (hour)
\(1.5\) hours = \(1\) hours \(30\) minutes.
Answer: \(1\) hours \(30\) minutes.
3. Solve problem 3 page 172 Math textbook 5
Two cars start from A and B at the same time and travel in opposite directions, after \(2\) hours they meet. Distance AB is \(180\text{km}\). Find the speed of each car, knowing that the speed of the car going from A is \(\dfrac{2}{3}\) the speed of the car going from B.
Solution method
Step 1: Calculate the total speed of the two cars (take the distance \(180km\) divided by the time the two cars meet)
Step 2: Draw a diagram showing the velocity relationship of the two cars
Step 3: Calculate the velocity of each car
Solution guide
The total velocities of the two cars are:
\(180 : 2 = 90\;(km/\) hours)
We have a diagram:
According to the diagram, the total number of equal parts is:
\(2 + 3 = 5\) (part)
The speed of the car going from A is:
\(90 : 5 × 2 = 36\) \((km/\)hour)
The speed of the car going from B is:
\(90 – 36 = 54\) \((km/\)hour)
Answer: Car goes from A: \(36km/\)hour; Car goes from B: \(54 km/\)hour.
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