Question

Sheriff Aniskin receives confidential information: the thief with the stolen accordion
has been traveling on a raft for 2 hour 40 minutes from Village Ivanovo toward
Village Sosnovka. Aniskin immediately leaves Sosnovka in a motorboat and travels
upstream toward the raft. Aniskin catches the thief 27 km from Sosnovka. Find the
speed of the raft if the speed of the motorboat in still water is 12 km/h and the
distance from Ivanovo to Sosnovka is 44 km.

Answer 1

The speed of the raft if the speed of the motorboat in still water is 3 km/h

What is speed?

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.

Let the speed of the raft (current) - r

Speed of motorboat - 12 km/h

The distance between villages - is 44 km

Let the time spent by Aniskin  - t

The time the thief was in travel = 2 hr 40 min + t = 2 40/60 + t = 3/8 + t

The distance the thief traveled = 44 - 27 = 17 km

We have the following equations:

r(8/3 + t) = 17

(12 - r)t = 27

Simplify the equations:

r(8/3 + t) = 17 ⇒ rt + 8/3r = 17

(12 - r)t = 27 ⇒ 12t - rt = 27

Add up the equations and solve for r:

rt + 8/3r + 12t - rt = 44

8/3r + 12t = 44

r = 16.5 - 4.5t

Substitute r into the second equation:

(12 - 16.5 + 4.5t)t = 27

4.5t² - 4.5t = 27

9t² - 9t - 54 = 0

Solving we get

t = 3 h

Find r:

r = 16.5 - 4.5*3 = 3 km/h

Therefore the speed of the raft if the speed of the motorboat in still water is 3 km/h

To know more about Speed follow

https://brainly.com/question/6504879

#SPJ1