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An elephant traveled 7 miles at an avera...

An elephant traveled 7 miles at an average rate of 4 miles per hour and then traveled the next 7 miles at an average rate of 1 mile per hour. What was the average speed, in miles per hour, of the elephant for the 14 miles?

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To find the average speed of the elephant for the total distance of 14 miles, we can follow these steps: ### Step 1: Calculate the time taken for the first 7 miles The elephant traveled the first 7 miles at an average speed of 4 miles per hour. We can use the formula: \[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \] For the first part: - Distance \(d_1 = 7\) miles - Speed \(s_1 = 4\) miles per hour So, the time taken \(t_1\) is: \[ t_1 = \frac{d_1}{s_1} = \frac{7}{4} \text{ hours} \] ### Step 2: Calculate the time taken for the second 7 miles The elephant then traveled the next 7 miles at an average speed of 1 mile per hour. Using the same formula: For the second part: - Distance \(d_2 = 7\) miles - Speed \(s_2 = 1\) mile per hour So, the time taken \(t_2\) is: \[ t_2 = \frac{d_2}{s_2} = \frac{7}{1} = 7 \text{ hours} \] ### Step 3: Calculate the total time taken for the entire journey Now, we can find the total time taken \(T\) by adding \(t_1\) and \(t_2\): \[ T = t_1 + t_2 = \frac{7}{4} + 7 \] To add these, we convert 7 into a fraction with a denominator of 4: \[ 7 = \frac{28}{4} \] Now, we can add: \[ T = \frac{7}{4} + \frac{28}{4} = \frac{35}{4} \text{ hours} \] ### Step 4: Calculate the average speed for the total distance The average speed \(S\) is given by the formula: \[ S = \frac{\text{Total Distance}}{\text{Total Time}} \] The total distance is 14 miles, and the total time is \(\frac{35}{4}\) hours: \[ S = \frac{14}{\frac{35}{4}} = 14 \times \frac{4}{35} = \frac{56}{35} \] Now, we can simplify \(\frac{56}{35}\): \[ S = \frac{56 \div 7}{35 \div 7} = \frac{8}{5} \text{ miles per hour} \] ### Step 5: Convert to decimal To convert \(\frac{8}{5}\) to decimal: \[ \frac{8}{5} = 1.6 \text{ miles per hour} \] ### Final Answer The average speed of the elephant for the 14 miles is **1.6 miles per hour**. ---
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