A person runs
1
4
of a mile in
1
32
of an hour. Compute the unit rate by setting up a complex fraction and simplifying
yes I mean 1/4 of a mile in 1/32 of an hour
I am supposed to figure out the speed.
(1/4)/(1/32) = 1/x
Cross multiply and solve for x.
To compute the unit rate, we need to determine the amount of distance covered per unit of time. In this scenario, the distance covered is
1
4
of a mile, and the time taken is
1
32
of an hour.
We can set up the complex fraction by placing the distance over time, like this:
(
1
4
miles
/
1
32
hour
)
To simplify the complex fraction, we need to multiply the numerator and denominator by the reciprocal of the denominator. The reciprocal of
1
32
is
32
1
or simply
32
. Multiplying the numerator and denominator by
32
gives:
(
1
4
miles
/
1
32
hour
)
x
(
32
32
)
Simplifying the result gives:
(
1
4
miles
)
x
(
32
1
)
Now, we can multiply the numerators and denominators:
(
1
x
32
)
/
(
4
x
1
)
This results in:
32/4
Finally, we simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 4. Dividing
32
and
4
by
4
gives:
8/1
Therefore, the unit rate is
8
miles per hour.
Do you mean ?
runs 1/4 of a mile in 1/32 of an hour