a band marches 2 1/2 miles in 1 2/3 hours at a juneteenth parade. they march at the same rate in a fourth of…

a band marches 2 1/2 miles in 1 2/3 hours at a juneteenth parade. they march at the same rate in a fourth of july parade for 1/2 hour. how far does the band march in 1/2 hour? type a number in each box. mile(s)

a band marches 2 1/2 miles in 1 2/3 hours at a juneteenth parade. they march at the same rate in a fourth of july parade for 1/2 hour. how far does the band march in 1/2 hour? type a number in each box. mile(s)

Answer

Explanation:

Step1: Convert mixed - numbers to improper fractions

$2\frac{1}{2}=\frac{2\times2 + 1}{2}=\frac{5}{2}$ and $1\frac{2}{3}=\frac{1\times3+2}{3}=\frac{5}{3}$.

Step2: Calculate the marching rate

The rate $r=\frac{\text{distance}}{\text{time}}$. So $r=\frac{\frac{5}{2}}{\frac{5}{3}}=\frac{5}{2}\times\frac{3}{5}=\frac{3}{2}$ miles per hour.

Step3: Find the distance in $\frac{1}{2}$ hour

Distance $d = r\times t$. Substitute $r = \frac{3}{2}$ and $t=\frac{1}{2}$. Then $d=\frac{3}{2}\times\frac{1}{2}=\frac{3}{4}$ miles.

Answer:

$\frac{3}{4}$