Solve math textbook exercises 5 Lessons: Some types of learned problems

A cyclist travels in \(3\) hours, in the first hour \(12km\), the second hour \(18km\), the third hour covers half the distance traveled in two hours head. On average, how many kilometers does that person walk per hour?

Solution method

Step 1: Calculate the distance traveled in the third hour

Step 2: Calculate the average distance traveled per hour by the car in an hour (equal to the total distance traveled by the car in three hours and then divided by three)

Solution guide

The distance covered by the cyclist in the third hour is:

\((12 + 18) : 2 = 15 \, (km)\)

The average distance traveled by a cyclist per hour is:

\((12 + 18 +15) : 3 = 15 \, (km)\)

Answer: \(15km\)

2. Solve problem 2 page 170 Math textbook 5

A rectangular piece of land has perimeter \(120m\). The length is greater than the width \(10m\). Calculate the area of ​​land.

Solution method

Step 1: Calculate half the perimeter of the rectangular plot.

Step 2: Calculate the length and width of the plot.

Step 3: Calculate the area of ​​the land.

Solution guide

Half the perimeter of the rectangular plot is:

\(120 : 2 = 60 \, (m)\)

The length of the rectangular garden is:

\((60 + 10) : 2 = 35 \, (m)\)

The width of the rectangular garden is:

\((60 – 10) : 2 = 25 \, (m)\)

(or \(60 – 35 = 25\))

The area of ​​that land is:

\(35 \times 25 = 875 \, (m^2)\)

Answer: \(875m^2\)

3. Solve problem 3 page 170 Math textbook 5

A block of metal has volume \(3.2cm^3\) and weight \(22.4g\). How many grams does a block of metal of the same substance with volume \(4.5cm^3\) weigh.

Solution method

Step 1: Calculate how many grams of the metal \(1cm^3\)

Step 2: Calculate the mass of a metal block with volume \(4.5cm^3\)

Solution guide

\(1cm^3\) heavy metals are:

\(22.4 : 3.2 = 7 \,(g)\)

\(4,5cm^3\) heavy metals are:

\(7 \times 4.5 = 32.5 \, (g)\)

Answer: \(31.5g\)