# Algebra - math word problems

1. Two runners Two runners ran simultaneously towards each other from locations distant 34.6 km. The average speed of the first runner was 1/5 higher than the average speed of the second runner. How long should each ran a 34.6 km, if you know that they meet after 67 m
2. Rectangle - sides What is the perimeter of a rectangle with area 266 cm2 if length of the shorter side is 5 cm shorter than the length of the longer side?
3. Pedestrian Pedestrian came started at 8h in the morning with speed 4.4 km/h. At half-past eleven cyclist started at 26 km/h same way. How many minutes take cyclist to catch up pedestrian?
4. Square If we increase one side of square by its one-half then square perimeter increase by 10 cm. What is the side of the square?
5. Parquet floor Three workers laid parquet floor for 2.301 hour. The first one would do this work alone 7 hours, the second in 6 hours. For how many hours would fulfill this work the third worker, if he worked alone?
6. Painters First painter painted fence himself for 4 hours, the second painter 1.2 hours sooner than first, and the third painters slowest up to 16 hours. How long took them paint fence if worked together?
7. Bottle Bottle with wine costs 58 USD. Wine is 27 USD more expensive than the empty bottle. How much is the bottle itself?
8. Parabola Find the equation of a parabola that contains the points at A[6; -5], B[14; 9], C[23; 6]. (use y = ax2+bx+c)
9. Swimming pool The pool shape of cuboid is 299 m3 full of water. Determine the dimensions of its bottom if water depth is 282 cm and one bottom dimension is 4.7 m greater than the second.
10. Coffee Coffee from the machine in the cup cost 28 cents. Coffee is 20 cents more expensive than the cup. How much is the cup?
11. 7 triangle The triangle area is 26.7 cm2. Determine the side length l if appropriate height hl = 45.3 cm.
12. Drive At the bus stop 8 people take out and 10 people take into bus. Next stop 6 take out and 5 take in. On the third stop 6 take out and 3 take in. The bus traveled further with 39 people. How many passengers were originally at the bus?
13. Population The town has 65,000 inhabitants. 40 years ago there were 157,000. How many people will live in town in 10 years if the average rate in population is as in previous years?
14. Linear independence Determine if vectors u=(-4; -5) and v=(20; 25) are linear Linear dependent.
15. Column Perpendicular pole high 8 m tall broke and its toe fell 2.7 m from the bottom of the pole. At what height above the ground pole broke?
16. Rhombus The rhombus with area 68 has one diagonal is longer by 6 than second one. Calculate the length of the diagonals and rhombus sides.
17. Circle chord Determine the radius of the circle in which the chord 6 cm away from the center of the circle is 12 cm longer than the radius of the circle.
18. Train and car The train and the car started at a constant speed to journey. When the train travels 87 km, the car travels 97 km. How many km travels the train when the car travels 87 km?
19. Deposit If you deposit 719 euros the beginning of each year, how much money we have at 1.3% (compound) interest after 9 years?
20. Mine What is temperature in the mine at a depth of 1160 m, where at depth 9 m is 11°C and every 100 m, the temperature increases by 0.7°C?

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