Rate

Advanced Math 5 · Unit 14 · unit-rate-work · Teacher edition

unit-rate-work

Name ______________________________Date ______________

1.
A bus travels $180$ km in $3$ hours. What is its speed, in km per hour?
Answer: ______________
2.
Ali can paint a fence in $4$ hours. Bea can paint the same fence in $12$ hours. Working together at these rates, how many hours do they take to paint the fence?
Answer: ______________
3.
A pump fills $\dfrac{3}{4}$ of a tank in $2$ hours. At this rate, how many hours does it take to fill the whole tank?
1. (A)
  $1\frac{1}{3}$
2. (B)
  $1\frac{1}{2}$
3. (C)
  $2\frac{2}{3}$
4. (D)
  $2\frac{3}{4}$

Answer key — Rate

1.
60unit-rate-work-01
$180 \div 3 = \mathbf{60}$ km/h.
2.
3unit-rate-work-02
Combined rate $= \frac{1}{4} + \frac{1}{12} = \frac{1}{3}$ fence per hour, so the whole fence takes $\mathbf{3}$ hours. (Adding the times, $4 + 12 = 16$ , cannot be right: together they must be faster than Ali alone.)
3.
(C)
$2\frac{2}{3}$
unit-rate-work-03
Rate $= \frac{3}{8}$ tank per hour. Time for $1$ tank $= 1 \div \frac{3}{8} = \frac{8}{3} = \mathbf{2\tfrac{2}{3}}$ hours. Or: each $\frac{1}{4}$ tank takes $\frac{2}{3}$ h, and four quarters take $\frac{8}{3}$ h. ( $1\frac{1}{3}$ treats $\frac{3}{4}$ as the hourly rate; $1\frac{1}{2}$ is $\frac{3}{4} \times 2$ ; $2\frac{3}{4}$ just adds the two numbers.)