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Grade 5 - Mathematics
12.1 Rates and Speed

Distance = Rate x Time
This formula can be written in different ways: To find rate, divide through on both sides by time:

Rate = Distance / Time
Rate is distance (given in units such as miles, feet, kilometers, meters, etc.) divided by time (hours, minutes, seconds, etc.).
Rate can always be written as a fraction that has distance units in the numerator and time units in the denominator, e.g., 25 miles/1 hour.

Time = Distance / Rate
When using this equation, it's important to keep the units same.
For instance, if the rate the problem gives is in miles per hour (mph), then the time needs to be in hours, and the distance in miles.
If the time is given in minutes, then divide by 60 to convert it to hours before you can use the equation to find the distance in miles.

Speed is defined as rate of change of distance. Speed is found using the formula: Speed = Distance / Time

  1. Speed is defined as rate of change of distance.
  2. Speed is found using S = D/T (S = Speed, D = Distance, T = Time)
  • A factory worker is paid $96 for working 8 hours. What is his rate?
    For 1 hour, he is paid $96/8 = $12.
    Answer: He is paid the rate of $12 per hour.
  • If a car travels 55 mph for 5 hour. Find the distance the car travelled.
    Speed = D/T
    D = S x T
    D = 55 x 5
    Answer: 275 m

Directions: Solve the following. Also write at least 10 examples of your own.
Q 1: A train is travelling at 2 km/min. How long will it take to travel 86 km? (hint D = r x t)

Q 2: An aeroplane travels 550 mi/h for 4 hours. How far did it travel. (hint D = r x t)
2200 miles
2000 miles
550 miles

Q 3: A train travels 195 miles in 3 hours. Find the distance traveled in 1 hour.
64 mi/h
65 mi/h
63 mi/h

Q 4: If a car travels 1,125 mi at 125 mph. Find the time.
7 hours
8 hours
9 hours

Q 5: What is a rate
is the ratio between two different quantities
is ratio between two equal quantities

Q 6: There are 5 girls to 9 boys in girl scout troop 123. Which ratio is the correct?
5 to 9

Q 7: Distance =
rate x time
rate x rate
rate + time

Q 8: Jim drove 220 miles in 4 hours on Tuesday. What was his average rate of speed?
85 mph
55 mph
65 mph

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Question 10: This question is available to subscribers only!

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