Question

a car is traveling at a constant speed. find the number of miles the car travels in 1 hour at the given rate.\\(\frac{100}{3}\\) miles in \\(\frac{2}{3}\\) hour
miles
to determine the number of miles for one hour, we divide the miles by the hours. recall, when dividing fractions be sure to mul the reciprocal.
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Explanation:

Step1: Recall the formula for speed

Speed \( v \) is given by the formula \( v=\frac{\text{distance}}{\text{time}} \). Here, the distance is \( \frac{100}{3} \) miles and the time is \( \frac{2}{3} \) hour. So we need to calculate \( v=\frac{\frac{100}{3}}{\frac{2}{3}} \).

Step2: Divide the fractions

When dividing fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of \( \frac{2}{3} \) is \( \frac{3}{2} \). So \( \frac{\frac{100}{3}}{\frac{2}{3}}=\frac{100}{3}\times\frac{3}{2} \).

Step3: Simplify the expression

The 3 in the numerator and the 3 in the denominator cancel out. So we have \( \frac{100}{2} = 50 \).

Answer:

50