Final answer:
The band would travel 0.75 miles in 1/2 hour.
Step-by-step explanation:
To find how far the band would travel in 1/2 hour, we can use the rate given in the problem. The band marches at 2 and 1/2 miles in 1 and 2/3 hours, so we can set up a proportion:
2.5 miles / 1 and 2/3 hours = x miles / 1/2 hour
To solve this proportion, we can cross-multiply:
(2.5 miles)(1/2 hour) = (1 and 2/3 hours)(x miles)
1.25 miles = (5/3)(x miles)
To solve for x, we can divide both sides of the equation by 5/3:
x miles = 1.25 miles ÷ (5/3) = 1.25 miles × (3/5) = 0.75 miles
Therefore, the band would travel 0.75 miles in 1/2 hour.