if a man jobs 3 1/2 miles in 3/4 of an hour, how far can he jog in one hour?
3 1 / 2 = 3 + 1 / 2 = 3 + 2 / 4 = 12 / 4 + 2 / 4 = 14 / 4
( 14 / 4 ) / ( 3 / 4 ) = 14 ∙ 4 / ( 3 ∙ 4 ) = 14 / 3 =
( 12 + 2 ) / 3 = 12 / 3 + 2 / 3 = 4 + 2 / 3 = 4 2/3
OR
3 1/2 / ( 3 / 4 ) = x / 1
x = 3 1/2 / ( 3 / 4 )
x = ( 14 / 4 ) / ( 3 / 4 ) = 14 ∙ 4 / ( 3 ∙ 4 ) = 14 / 3 =
( 12 + 2 ) / 3 = 12 / 3 + 2 / 3 = 4 + 2 / 3 = 4 2/3
OR
1 h / ( 3 / 4 ) h = ( 4 / 4 ) / ( 3 / 4 ) = ( 4 ∙ 4 ) / ( 4 ∙ 3 ) = 4 / 3
( 4 / 3 ) ∙ 3 1 / 2 = ( 4 / 3 ) ∙ ( 14 / 4 ) = 4 ∙ 14 / ( 4 ∙ 3 ) = 14 / 3 =
( 12 + 2 ) / 3 = 12 / 3 + 2 / 3 = 4 + 2 / 3 = 4 2/3 mi
To find out how far the man can jog in one hour, you need to determine his jogging speed. The given information tells us that the man jogs 3 1/2 miles in 3/4 of an hour.
To calculate the distance he can jog in one hour, you can set up a proportion. A proportion is an equation stating that two ratios are equal. In this case, the ratio of distance to time should be the same for both amounts.
Let 'x' represent the distance the man can jog in one hour. The proportion can be set up as follows:
3 1/2 miles / 3/4 hours = x miles / 1 hour
To solve the proportion, you need to convert the mixed number 3 1/2 to an improper fraction. The improper fraction equivalent of 3 1/2 is 7/2.
Now, the equation becomes:
(7/2) miles / (3/4) hours = x miles / 1 hour
To divide fractions, you multiply by the reciprocal of the divisor. Therefore:
(7/2) * (4/3) = x
Multiplying the fractions, you get:
28/6 = x
Simplifying the fraction, you get:
14/3 = x
So, the man can jog approximately 14/3 miles in one hour.