Question

1. (standard 7.pr.2) jasmine is training for a race. she ran \\(\frac{3}{4}\\) of a mile in \\(\frac{1}{6}\\) of an hour. what is her constant running speed in miles per hour?

Explanation:

Step1: Recall speed formula

Speed \( v \) is given by the formula \( v=\frac{\text{distance}}{\text{time}} \). Here, distance \( d = \frac{3}{4} \) mile and time \( t=\frac{1}{6} \) hour.

Step2: Substitute values into formula

Substitute \( d=\frac{3}{4} \) and \( t = \frac{1}{6} \) into the speed formula: \( v=\frac{\frac{3}{4}}{\frac{1}{6}} \).

Step3: Divide fractions

Dividing by a fraction is equivalent to multiplying by its reciprocal, so \( \frac{\frac{3}{4}}{\frac{1}{6}}=\frac{3}{4}\times6 \).

Step4: Simplify the multiplication

\( \frac{3}{4}\times6=\frac{3\times6}{4}=\frac{18}{4}=\frac{9}{2} = 4.5 \).

Answer:

\( \frac{9}{2} \) (or \( 4.5 \)) miles per hour