# Expression of a variable from formula - math word problems - page 21

1. The tourist
The tourist came started from the hostel at an average speed of 5km/h. Half an hour later, the bicyclist started along the same route at a speed of 20km/h. How many minutes will a cyclist catch up and how many kilometers will he go?
2. The coil
How many ropes (the diameter 8 mm) fit on the coil (threads are wrapped close together) The coil has dimension: the inner diameter 400mm, the outside diameter 800mm and the length of the coil is 470mm
3. Area of garden
If the width of the rectangular garden is decreased by 2 meters and its length is increased by 5 meters, the area of the rectangle will be 0.2 ares larger. If the width and the length of the garden will increase by 3 meters, its original size will increas
4. The sides 2
The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid’s area is 245. Find the height and the perimeter of the trapezoid.
5. Cube surface and volume
Find the surface of the cube with a volume of 27 dm3.
6. Diamond diagonals
Find the diamond diagonal's lengths if the area is 156 cm2 and side is 13 cm long.
7. Nonagon
Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm
8. Pyramid cut
We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has a content of 10 cm2. Find the area of the o
9. Cuboid walls
If the areas of three adjacent faces of a cuboid are 8 cm², 18 cm² and 25 cm². Find the volume of the cuboid.
10. The painter
In order for the painter to get the desired color, he must mix green and yellow in a ratio of 4: 7. If it has 28 l of green color, how many liters of yellow color should he add? How many liters of mixed color does he get?
11. Soldier
An experienced soldier digs a good trench in 30 hours. Two soldiers dug the same trench each 40 hours. How many hours will the ditch dig all three together?
12. Rectangles
The perimeter of a rectangle is 90 m. Divide it into three rectangles, the shorter side has all three rectangles the same, their longer sides are three consecutive natural numbers. What is the dimensions of each rectangle?
13. Workers
Two workers will construct the stage at the festival in 54 hours. Organizers need to shorten the assembly time by 42 hours. How many workers must the assembly company send?
14. Cube diagonals
The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal.
15. Triangle perimeter
Calculate the triangle perimeter whose sides are in ratio 3: 5: 7 and the longest side is 17.5 cm long.
16. Diagonals of a rhombus 2
One diagonal of a rhombus is greater than other by 4 cm . If the area of the rhombus is 96 cm2, find the side of the rhombus.
17. Car driver
The car driver is in town A and is scheduled to be in town B at a specified hour. If it travels at an average speed of 50km/h, it will arrive in city B 30 minutes later. But if he travels at an average speed of 70km/h, he would arrive half an hour earlier
18. Two pipes
How long will the pool be filled with a double supply pipe if it takes the pool to fill the first pipe by 4 hours longer and the second pipe 9 hours longer than both pipes open at the same time?
19. Peroxide
How many ml 30% of peroxide (H2O2) should be poured into 100ml H2O to give a 20% solution?
20. Children playground
The playground has the shape of a trapezoid, the parallel sides have a length of 36 m and 21 m, the remaining two sides are 14 m long and 16 m long. Determine the size of the inner trapezoid angles.

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