Expert: Chen Min - 5/5/2008

Question
1. Some students planned for a get-together. The budget for food was $5... Five of the students failed to come because of the distance and therefore the cost of food for each member increased by $5. How many students attended the get-together?

2. Steve traveled 600 miles at a certain speed. Had he gone  20mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle.

3.Rita rows 12 km upstream in 3 hours. The speed of her boat in still water is 9 km/hr. Find the speed of the stream.

Answer
1.Assume there were x students to come in the plan,
 the total food price = 5x
 the actual number of students = x-5
 the total food price = 10(x-5)
 as the total food price does not change,
 5x = 10(x-5)
 x = 10....quadratic???

2.Assume the speed is v mph,
 600/v ```````his time on the trip
 600/(v + 20)``````````his expected time on trip
 1`````````the difference in time taken.

 Hence 600/v = 600/(v+20) + 1
 Simplify it, vē+20v-12000 = 0
 Factorise it, (v+120)(v-100) = 0
 As v must be positive, v=100

3.Assume he's rowing in still water, then in 3 hrs, he should've                    
 advanced 3*9 = 27km
 The water opposing him "dragged" him 27-12 = 15km
 The speed of water is 15/3 = 5km/h
 (This question is not about quadratic equation, I reckon...)

Hope this helps:)