Algebra
If you run half the distance of a race at 6 mph, how fast do you need to run the remaining half of the race to average 12 mph for the entire distance?
It is impossible to average 12 mph after running the first half at 6 mph, as you would need infinite speed for the second half.
A specialty shop wants a 280-pound nut mixture (peanuts $1.20/lb, almonds $2.20/lb, cashews $3.20/lb) costing $2.59/lb. The weight of almonds and cashews combined must be three times the weight of peanuts. Find the pounds of each nut.
The shop needs 70 pounds of peanuts, 30.8 pounds of almonds, and 179.2 pounds of cashews to create the specified mixture.