Big Ideas Math: Modeling Real Life, Grade 8
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Big Ideas Math: Modeling Real Life, Grade 8 View details
4. Zero and Negative Exponents
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Exercise 19 Page 340

Start by writing the length of the garden in feet.

15 minutes, see solution.

Practice makes perfect

We know that a snail travels through our garden with a constant speed. A garden is 12 yards long and the snail moves with a speed of 5^(- 2) feet per second. We want to know how much time the snail needs to travel through the length of the garden.

Distance Rate (Speed)
d =12 yards r =5^(- 2) feet/second
First, we should express the given values in the same unit. Let's start by writing the length of the garden in feet. Remember the relationship between yards and feet. 1 yard = 3 feetBecause 1 yard is 3 feet, we can rewrite the length of the garden in feet. 12 yards = 12 * 3 feet Let's evaluate this expression!
12 * 3 feet
36 feet
Having the length of the garden in feet, we can calculate the time it takes the snail to travel through the length of the garden. To find the time we will use the distance-time equation.
Words Symbols
distance = rate * time d = r * t
In our case distance d is 36 feet and rate, or speed, r is 5^(- 2) feet per second. We can substitute these values into the formula and solve for t. Let's start by rewriting the negative exponent!
d = r * t
36 = 5^(- 2) * t
36 = 1/5^2 * t
36 = 1/25 * t
36 = t/25
36 * 25 = t/25 * 25
36 * 25 = t
900 = t
t = 900
We found the time in seconds but we need to express it in minutes. Recall that each 60 seconds is 1 minute. If we divide the number of seconds the snail needs to travel through the garden by 60, we will find its time in minutes. 900 seconds = 900/60 minutes Let's evaluate this quotient!
900/60 minutes
15 minutes
The snail needs 15 minutes to travel through the garden.