Question

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

Explanation:

Answer 2

• 3 km/h

Explanation:

• Let the speed of raft (current) - r
• Speed of motorboat - 12 km/h
• The distance between villages - 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 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 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