The speed of a vehicle is inversely proportional to the time it takes to travel a fixed distance.

Question

The speed of a vehicle is inversely proportional to the time it takes to travel a fixed distance. If a vehicle travels a fixed distance at45miles per hour in15minutes, how fast must it travel to cover the same distance in25minutes

my answer sheet says its 27, but im not sure how my teacher got that.

Answer 1

Since this is an inverse relationship the following holds true: (X1)(Y1) = (X2)(Y2)

If X1 is 45 mph, Y1 is 15 min, and Y2 is 25 min then we have the following equation

(45 mph) (15 min) = X2 (25 min)

and dividing both sides by 25 min X2 value is 27 mph.

Answer 2

Distance = Rate x Time (Rate is speed).

D/T = R

Situation 1: Distance = 45 miles/hour x 1/4 hour (15 minutes = 1/4 hour)

Distance = 45 * 1/4 = 45/4 miles.

45/4 = Rate x 25 minutes

25 minutes = 25/60 hours = 5/12 hours.

45/4 = Rate x 5/12

12/5 x 45/4 = Rate in miles per hour.

12/5 x 45/4 = 3 x 9 = 27 miles per hour.