Math 121, Quiz 2, October 1, 2004
Name: Hints and Answers
Instructions. Do all problems, and show all of your work. Calculators are not allowed.
1. (2 pts) A worker can build a fence in 11 hours. With the help of an assistant, the fence can
be built in 7 hours. How long would it take the assistant to build the fence alone?
Answer. Let Abe the amount of time in hours that it takes the assistant to build the fence
alone. Then 7
11 +7
A= 1
Therefore, 7
A=4
11 and so A=77
4.
That is, the assistant could complete the fence in 19 hours and 15 minutes working alone.
2. (2 pts) Solve the equation 3x−6 = 2x2by the method of your choice.
Answer. The equation is equivalent to 2x2−3x+ 6 = 0 and so by the quadratic formula
x=3±p32−4(2)(6)
2(2) =3±i√39
4.
3. (2 pts) Solve the inequality |3−4x|>17. Write your answer in interval form.
Answer. The inequality is equivalent to:
3−4x > 17 or 3 −4x < −17
−4x > 14 or −4x < −20
x < −7
2or x > 5
In interval form, the solution is (−∞,−7
2)∪(5,∞).
4. (2 pts) The distance of a motorcycle jump varies directly as the square of its velocity.
(a) Write the relation for this.
Answer. d=kv2where kis a constant.
(b) If the velocity of the motorcycle is tripled, how does the distance change?
Answer. Distance increases by a factor of 32, i.e. the distance of the jump will be 9 times
greater than the original jump.