Question

The time it takes a car to travel a certain distance is inversely related to the rate at which the car
traveled. Benita drives a race car around a race track. At a constant speed of 180 miles per hour
she can finish the entire race in half an hour.
At what rate did Benita travel if she completed the race in 15 minutes?
A 400 miles per hour
B 360 miles per hour
C 320 miles per hour
D 300 miles per hour
The answer is B but idk how!?

Answer 1

time is inversely related to rate so \[t = \frac kr\]
where t is time; r is rate; k is proportionality constant

when the speed is 180 then the time is 30 minutes so r = 180 and t = 30
\[30 = \frac{k}{180}\]
solve for k
\[30 \times 180 = k\]
\[k = 5400\]

now for the second situation t = 15 and you're asked to look for r
\[t = \frac kr\]
\i can also write this as \[r = \frac kt\]
so let us solve for r \[r = \frac{5400}{15}\]
\[r = 360\]
does that help?