Question

​ Yesterday, Noah ran 2 and one half miles in three fifths hour. Emily ran 3 and three fourths miles in five sixths hour. Anna ran 3 and one half miles in three fourths hour . What was the unit rate for miles per hour for each​ person? Who ran the​ fastest? Use pencil and paper. Describe two ways you can find who ran the fastest.

Answer 1

Answer:

Step-by-step explanation:

S (distance) is the product of unit rate (or velocity) and time.

S = V × t => V = S/t

* Noah ran S1 = 2$\frac{1}{2}$ = 3/2 miles in t1 = $\frac{3}{5}$ hour.

Therefore, the unit rate for miles per hour for Noah is

V1 = S1/t1 = $\frac{3}{2} : \frac{3}{5}$ = $\frac{3}{2} × \frac{5}{3}$ = 5/2 = 2.5 miles/hour

* Emily ran S2 = 3$\frac{3}{4}$ = 15/4 miles in t2 = $\frac{5}{6}$ hour.

Therefore, the unit rate for miles per hour for Emily is

V2 = S2/t2 = $\frac{15}{4} : \frac{5}{6}$ = $\frac{3}{2} × \frac{6}{5}$ = 9/2 = 4.5 miles/hour

* Anna ran S3 = 3$\frac{1}{2}$ = 7/2 miles in t3 = $\frac{3}{4}$ hour.

Therefore, the unit rate for miles per hour for Anna is

V3 = S3/t3 = $\frac{7}{2} : \frac{3}{4}$ = $\frac{7}{2} × \frac{4}{3}$ = 14/3 = 4.7 miles/hour

V1 < V2 < V3

=> Anna ran fastest among the three people.