Rate and speed

Advanced Math 6 · Unit 6 · rate-speed · Teacher edition

rate-speed

Name ______________________________Date ______________

1.
A car travels $180$ km in $2.5$ hours. What is its speed in km/h?
Answer: ______________
2.
Apples cost $7.50 for $5$ pounds. What is the price per pound, in dollars?
Answer: ______________
3.
Convert $20$ m/s to km/h.
Answer: ______________
4.
A cyclist rides at $60$ km/h for $1$ hour, then at $40$ km/h for $2$ hours. What is the average speed for the whole ride?
1. (A)
  $50$ km/h
2. (B)
  $46\tfrac{2}{3}$ km/h
3. (C)
  $48$ km/h
4. (D)
  $100$ km/h
5.
Jo walks $3$ km to school at $4$ km/h and takes the bus back along the same road at $12$ km/h. What is Jo's average speed for the round trip, in km/h?
Answer: ______________

Answer key — Rate and speed

1.
72rate-speed-01
$180 \div 2.5 = \mathbf{72}$ km/h. Check: $72 \times 2.5 = 180$ . ✓
2.
1.5rate-speed-02
$7.50 \div 5 = \mathbf{1.50}$ dollars per pound.
3.
72rate-speed-03
$20 \times 3600 = 72{,}000$ m per hour $= \mathbf{72}$ km/h. Shortcut: multiply m/s by $3.6$ .
4.
(B)
$46\tfrac{2}{3}$ km/h
rate-speed-04
Total distance $140$ km, total time $3$ h: $\frac{140}{3} = \mathbf{46\tfrac{2}{3}}$ km/h. The answer is closer to $40$ than to $60$ because more time was spent at $40$ . ( $50$ is the trap: averaging the speeds.)
5.
6rate-speed-05
Total time $= \frac{3}{4} + \frac{1}{4} = 1$ hour for $6$ km, so the average speed is $\mathbf{6}$ km/h — not $8$ , the mean of $4$ and $12$ . Jo spends three times as long walking as riding, so the slow speed dominates.