problem solving?

Question

pls. help.pls show me the solutions.. tnx
Pls. help me solve dis..


1. Find the length of the side of an equilateral triangle whose altitude is 3cm shorter than a side.

2. An airplane flies 900 km against a head wind of 25kph. The plane took 15 minutes longer for this flight than with a tail wind of 25kph. How fast could the plane fly in still air?

3.Fifty-four cans are packed in some boxes so that the number of boxes is more than the number of cans in each box. Find the number of boxes used.

4. Dean and Len can type a manuscript together in 3 and 3/5 hours. Dean, working alone can type the manuscript 3 hours longer than Len. How long would it take each to type the manuscript alone?

5. A mango grove has 20 trees per acre, and the average yoeld is 300 mangoes per tree. For each additional tree per acre, the average yield will be reduced by 10 mangoes per tree. How many trees per acre will yield the maximum number of mangoes per acre, and what is the maximum number of mangoes per acre?

Answer 1

1. When you draw the altitude of an equilateral triangle, you create two 30-60-90 triangles. So if the side is s, then the altitude is s-3. Since this is part of a 30-60-90 triangle, the smallest side is (s/2) and the altitude is (s√3)/2. Set (s√3)/2 equal to s-3 and solve.

2. Let "s" be the speed in still air. Then its speed against the wind is s-25 and with the wind is s+25. Use the relationship speed = distance / time to find a way to relate to the time differences.

3. If there are B boxes used and C cans in each box, then BC = 54. Also, we're told B > C. There are lots of different answers to this, even if we restrict B and C to being integers. Find different factor pairs of 54.

4. Since it takes 3 times as long for Dean to do what Len can do in the same amount of time, then if Len can type m manuscripts in one hour, then Dean can type m/3 manuscripts in one hour. So in 3 3/5 hours (or 18/5 hours), Len types m(18/5) manuscripts and Dean types (m/3)(18/5) manuscripts. Add these together and set the sum equal to 1 (for the one manuscript they can complete in 18/5 hours). Solve for m, then find m/3.

5. Right now the number of mangoes per acre is 20*300. If you add t more trees, you get (20 + t) trees making (300 - 10t) mangoes each. So the new total is (20 + t)(300 - 10t). Simplifiy this expression and set it equal to y. Then graph y over y. You'll notice that this is an upside-down parabola, so the maximum value of y (which is where it peaks) tells you what the corresponding t value should be.

Answer 2

That's an awful lot of homework for 10 points. Here's #1.

The altitude forms two 30/60/90 right triangles. If x is the side of such a triangle, the hypotenuse, side opposite the 30 deg angle and the altitude will be in the ratio x, x/2, and x/2*sqrt(3) respectively. So x/2*sqrt(3) +3 = x.
Solve for x.