Question

The faster you drive the less time it takes to reach your destination (a driver's speed is inversely proportional to the drive time). Mike takes 45 minutes to

travel from point a to point b at 60 miles and hour. Kelly takes the same trip at 80 miles an hour. How long does the trip take Kelly? (Round to the nearest
whole number)

Answer 1

The time the trip takes Kelly is approximately 34 minutes

Explanation:

The topic examined by the question is the relationship between speed, distance traveled, and time which is presented here as follows;

`Speed, \ S = (Distance \ travelled \ 'd')/(Time \ taken \ 't')`

The given parameters of the journey are;

The time it takes Mike to travel from point 'a' to point 'b' = 45 minutes

The speed with which Mike travels = 60 miles an hour

The speed with which Kelly travels the same trip = 80 miles an hour

Let 'd' represent the distance from point 'a' to point 'b', and let 't' represent the time the trip takes Kelly

For Mike, we have;

S = d/t

∴ d = S × t

Where;

S = 60 miles per hour

t = 45 minutes = 0.75 hour

d = 60 miles/hour × 0.75 hour = 45 miles

The distance from point 'a' to point 'b' = d = 45 miles

Similarly, from S = d/t, we have for Kelly the time 't' given as follows;

t = d/S

Where;

S = 80 miles/hour

d = 45 miles

∴ t = 45 miles/(80 miles/hour) = 9/16 hour = 9/16 hour × 60 min/hour = 33.75 minutes

The time the trip takes Kelly = 33.75 minutes ≈ 34 minutes.