# Ratio + system of equations - math problems

On solving problems and tasks with proportionally we recommend hint rule of three. Rule of three (proportionality) help solve examples of direct and inverse proportionality. Three members makes possible to calculate the fourth - unknown member.

1. Forestry workers In the forest is employed 56 laborers planting trees in nurseries. For 8 hour work day would end job in 37 days. After 16 days, 9 laborers go forth? How many days are needed to complete planting trees in nurseries by others, if they will work 10 hours a d
2. Excavation Mr. Billy calculated that excavation for a water connection dig for 12 days. His friend would take 10 days. Billy worked 3 days alone. Then his friend came to help and started on the other end. On what day since the beginning of excavation they met?
3. Motion If you go at speed 3.7 km/h, you come to the station 42 minutes after leaving the train. If you go by bike to the station at speed 27 km/h, you come to the station 56 minutes before its departure. How far is the train station?
4. Store One meter of the textile was discounted by 2 USD. Now 9 m of textile cost as before 8 m. Calculate the old and new price of 1 m of the textile.
5. Two squares Two squares whose sides are in the ratio 5:2 have sum of its perimeters 73 cm. Calculate the sum of area this two squares.
6. Right triangle Legs of the right triangle are in the ratio a:b = 2:8. The hypotenuse has a length of 87 cm. Calculate the perimeter and area of the triangle.
7. Rectangle - sides ratio Calculate area of rectangle whose sides are in ratio 3:13 and perimeter is 673.
8. Gear Two gears, fit into each other, has transfer 2:3. Centres of gears are spaced 82 cm. What are the radii of the gears?
9. Ships At 8:40 the ship set sail at 12 km/h. At 19:10 followed by at 29 km/h sail boat. When sail boat catches up the ship? How many minutes will catch up took?
10. Number ratio Calculate two positive numbers that its ratio is 6:6 and difference was 0.
11. Ratio 6 numbers are in the ratio 1:5:1:5:5:5. Their sum is 242. What are the numbers?
12. Pumps The tank is filled with two pumps in 16 minutes. The first pump is filled in 30 minutes earlier than two one. How many minutes is filled with the first pump?
13. Tea blend Tea blends are maked from two kinds of tea. In standard tea mixture are two teas in the ratio 1:3 and 40 g costs 42 CZK. In the premium tea mixture are weighing two teas in the ratio 1:1 and 50 grams costs 60 CZK. How much cost 10 grams of more expensive k
14. Division Three siblings Helena, Oliver and George split the bag with candies on merit in the ratio 6:1:4. How many candies should each get if in bag were 88?
15. Triangle angles The angles α, β, γ in triangle ABC are in the ratio 6:2:6. Calculate size of angles.
16. Car factory Carmaker now produce 2 cars a day more than last year, so the production of 70312 cars will save just one full working day. How many working days needed to manufacture 70312 cars last year?
17. Family and age ratios Age of father and son are in the ratio 10:3; age of father and daughter are in the ratio 5:2. How old is father and son, if daughter is 20 years old? In what ratio is age sister and brother?
18. Honza + Alice + Tonda Honza + Alice + Tonda have a total of 111 USD. The ratio between Honza and Alena is 5:6 and the ratio between Alice and Tonda is 4:5 How many money have each of them?
19. Chicken I threw three chicken for a handful of grains and I noticed that it eat in a ratio of 8:7:6 and two of them grabbed 156 grains. How many grains have fought that chicken?
20. Revenue Mr. Robert and Mr. Norbert get together € 1400. The revenue split in the ratio of 4:3, depending upon each work. How many got each of them?

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