Studdy AI Logo
Math  /  Algebra

QuestionA turtle travels 512\frac{5}{12} mile in 13\frac{1}{3} hour and a snail travels 18\frac{1}{8} mile in 34\frac{3}{4} hour. Which animal is faster? The turtle's rate is greater than 1 mile per hour.
The snail's rate is less than 1 mile per hour.
Find the turtle's speed in miles per hour.
The turtle's speed is mile(s) per hour.

Studdy Solution

STEP 1

1. The turtle travels 512\frac{5}{12} mile in 13\frac{1}{3} hour.
2. The snail travels 18\frac{1}{8} mile in 34\frac{3}{4} hour.
3. We need to determine which animal is faster.
4. We need to calculate the turtle's speed in miles per hour.

STEP 2

1. Calculate the turtle's speed in miles per hour.
2. Calculate the snail's speed in miles per hour.
3. Compare the speeds to determine which animal is faster.

STEP 3

Calculate the turtle's speed in miles per hour.
The turtle travels 512\frac{5}{12} mile in 13\frac{1}{3} hour. To find the speed, divide the distance by the time:
Turtle’s speed=512 mile13 hour\text{Turtle's speed} = \frac{\frac{5}{12} \text{ mile}}{\frac{1}{3} \text{ hour}}
To divide fractions, multiply by the reciprocal:
Turtle’s speed=512×31=5×312×1=1512=54 miles per hour\text{Turtle's speed} = \frac{5}{12} \times \frac{3}{1} = \frac{5 \times 3}{12 \times 1} = \frac{15}{12} = \frac{5}{4} \text{ miles per hour}

STEP 4

Calculate the snail's speed in miles per hour.
The snail travels 18\frac{1}{8} mile in 34\frac{3}{4} hour. To find the speed, divide the distance by the time:
Snail’s speed=18 mile34 hour\text{Snail's speed} = \frac{\frac{1}{8} \text{ mile}}{\frac{3}{4} \text{ hour}}
To divide fractions, multiply by the reciprocal:
Snail’s speed=18×43=1×48×3=424=16 miles per hour\text{Snail's speed} = \frac{1}{8} \times \frac{4}{3} = \frac{1 \times 4}{8 \times 3} = \frac{4}{24} = \frac{1}{6} \text{ miles per hour}

STEP 5

Compare the speeds to determine which animal is faster.
The turtle's speed is 54\frac{5}{4} miles per hour, and the snail's speed is 16\frac{1}{6} miles per hour.
Since 54>16\frac{5}{4} > \frac{1}{6}, the turtle is faster.
The turtle's speed is 54\frac{5}{4} miles per hour.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord