Here are some cool equations.
solutions will be added shortly (jan5)
the problems are not going in order of hardness, some problems are easier than others.
1) Twenty-five woman did 1/5 of a job in 8 days. Then, because of an emergency, it became necessary to compleate the job in the next 20 days.
How many additional woman needed to be added to the crew of 25 to accomplish this?
(mathcounts 1989)
2)When three numbers are added two at a time, the sums are 29, 46, 53.
What is the sum of all three numbers?
(mathcounts 1991)
3)Each valve A, B, C, when open, releases water into a tank at it's own constant rate. With all three valvespen, the tank fills in 1 hour, with only valves A and C open it takes 1.5 hour, and with only valves B and C open it takes 2 hours. How long will it take to fill the tank with only valves A and B?
(ASHME 1973)
4) One car left a city at 2:00 pm and traveled at an average speed of 40 miles per hour. A second car left at 4:00 pm, traveled at the same route and overtook the first car at 9:00 pm. What was the average speed in miles per hour of the second car??
(mathcounts 1991)
5) K takes 30 min less time than M to travell a distance of 30 miles. K traveles 1/3 mile per hour faster than M. If x is K's rate of speed in miles per hour, then find K's time for the distance in terms of x.
(ASHME 1952)