A turtle crawling at a rate of. 1 (mi) / (h) passess a resting bunny that rests for 30 minutes but moves 5 (mi) / (h). How many feet must the bunny run to catch the turtle

The bunny needs to run approximately 269.39 feet

Solution:

Let "x" be the number of hours passed since the turtle passed the buuny

Given that turtle crawls at a rate of 0.1 miles per hour

Then for "x" hours, distance traveled by turtle is 0.1x miles

Also given that bunny moves at 5 miles per hour but rests for 30 minutes

1 hour = 60 minutes

Therefore,

30 minutes = 0.5 hours

So the bunny rests for 0.5 hours

Thus the distance traveled by bunny is 5 (x - 0.5) miles

To find when they will pass each, set the two distances equal to each other

0.1x = 5 (x - 0.5)

0.1x = 5x - 2.5

5x - 0.1x = 2.5

4.9x = 2.5

x = 0.51

Thus the distance ran by buuny is:

Distance = 5 (x - 0.5)

Substitute x = 0.51

Distance = 5 (0.51020 - 0.5)

Distance = 5 (0.010) = 0.05102 miles

Convert to feet

1 mile = 5280 feet

0.05102 miles = 0.05102 x 5280 feet = 269.39 feet

Thus the bunny needs to run approximately 269.39 feet