QuestionСедедгөений бодлогууд Толын хоер зогсоолын хооронддл зай 60 км богоод моторт завь энэ зайг урегал дагуу 2 цатт, сорж 3 даг тудддаг. Моторт завины уурд болон урсгалын дурдыг ол.

Studdy Solution

STEP 1

1. The distance between the two docks is 60 km.
2. The motorboat takes 2 hours to travel downstream.
3. The motorboat takes 3 hours to travel upstream.
4. We need to find the speed of the motorboat in still water and the speed of the current.

STEP 2

1. Define variables for the speeds.
2. Write equations for downstream and upstream travel.
3. Solve the system of equations.

STEP 3

Define variables for the speeds.
Let $b$ be the speed of the motorboat in still water (in km/h). Let $c$ be the speed of the current (in km/h).

STEP 4

Write equations for downstream and upstream travel.
For downstream travel, the effective speed is $b + c$ and the time taken is 2 hours. The equation is:
$(b + c) \times 2 = 60$
For upstream travel, the effective speed is $b - c$ and the time taken is 3 hours. The equation is:
$(b - c) \times 3 = 60$

STEP 5

Solve the system of equations.
First, simplify the equations:
1. $2(b + c) = 60$ becomes $b + c = 30$
2. $3(b - c) = 60$ becomes $b - c = 20$
Now, solve the system of equations:
Add the two equations:
$(b + c) + (b - c) = 30 + 20$ $2b = 50$ $b = 25$
Substitute $b = 25$ into one of the original equations, for example, $b + c = 30$ :
$25 + c = 30$ $c = 5$
The speed of the motorboat in still water is $\boxed{25}$ km/h, and the speed of the current is $\boxed{5}$ km/h.

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