Math / Algebra

QuestionМоторт завь 2 зогсоолын хооронд урсгал дагуу 4 цаг, урсгал сөрж 5 цаг явна. Голын урсгалын хурд 2 км/ц бол зогсоолуудын хоорондох зайг ол.

Studdy Solution

STEP 1

1. The motorboat travels downstream for 4 hours and upstream for 5 hours.
2. The speed of the river current is 2 km/h.
3. We need to find the distance between the two docks.

STEP 2

1. Define variables for the speeds.
2. Write expressions for the downstream and upstream speeds.
3. Use the time, speed, and distance relationship to form equations.
4. Solve the equations to find the distance.

STEP 3

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

STEP 4

Write expressions for the downstream and upstream speeds.
- Downstream speed = $b + 2$ km/h (since the current aids the boat's speed). - Upstream speed = $b - 2$ km/h (since the current opposes the boat's speed).

STEP 5

Use the time, speed, and distance relationship to form equations. The distance traveled downstream and upstream is the same.
- Downstream: Distance = Speed $\times$ Time = $(b + 2) \times 4$ - Upstream: Distance = Speed $\times$ Time = $(b - 2) \times 5$
Since both distances are equal, we have:
$(b + 2) \times 4 = (b - 2) \times 5$

STEP 6

Solve the equation to find the speed of the boat in still water.
Expand both sides:
$4b + 8 = 5b - 10$
Rearrange to solve for $b$ :
$8 + 10 = 5b - 4b$ $18 = b$
The speed of the boat in still water is 18 km/h.

STEP 7

Now, calculate the distance using the downstream speed and time:
Distance = $(b + 2) \times 4 = (18 + 2) \times 4 = 20 \times 4 = 80$ km
The distance between the two docks is:
$\boxed{80}$ km

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QuestionМоторт завь 2 зогсоолын хооронд урсгал дагуу 4 цаг, урсгал сөрж 5 цаг явна. Голын урсгалын хурд 2 км/ц бол зогсоолуудын хоорондох зайг ол.

Studdy Solution

STEP 1

1. The motorboat travels downstream for 4 hours and upstream for 5 hours.
2. The speed of the river current is 2 km/h.
3. We need to find the distance between the two docks.

STEP 2

1. Define variables for the speeds.
2. Write expressions for the downstream and upstream speeds.
3. Use the time, speed, and distance relationship to form equations.
4. Solve the equations to find the distance.

STEP 3

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

STEP 4

Write expressions for the downstream and upstream speeds.
- Downstream speed = $b + 2$ km/h (since the current aids the boat's speed). - Upstream speed = $b - 2$ km/h (since the current opposes the boat's speed).

STEP 5

STEP 6

Solve the equation to find the speed of the boat in still water.
Expand both sides:
$4b + 8 = 5b - 10$
Rearrange to solve for $b$ :
$8 + 10 = 5b - 4b$ $18 = b$
The speed of the boat in still water is 18 km/h.

STEP 7

Now, calculate the distance using the downstream speed and time:
Distance = $(b + 2) \times 4 = (18 + 2) \times 4 = 20 \times 4 = 80$ km
The distance between the two docks is:
$\boxed{80}$ km

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QuestionМоторт завь 2 зогсоолын хооронд урсгал дагуу 4 цаг, урсгал сөрж 5 цаг явна. Голын урсгалын хурд 2 км/ц бол зогсоолуудын хоорондох зайг ол.

Studdy Solution

STEP 1

1. The motorboat travels downstream for 4 hours and upstream for 5 hours.2. The speed of the river current is 2 km/h.3. We need to find the distance between the two docks.

STEP 2

1. Define variables for the speeds.2. Write expressions for the downstream and upstream speeds.3. Use the time, speed, and distance relationship to form equations.4. Solve the equations to find the distance.

STEP 3

Define variables for the speeds. Let b b b be the speed of the boat in still water (in km/h).

STEP 4

Write expressions for the downstream and upstream speeds.- Downstream speed = b+2 b + 2 b+2 km/h (since the current aids the boat's speed). - Upstream speed = b−2 b - 2 b−2 km/h (since the current opposes the boat's speed).

STEP 5

STEP 6

Solve the equation to find the speed of the boat in still water.Expand both sides:4b+8=5b−10 4b + 8 = 5b - 10 4b+8=5b−10Rearrange to solve for b b b:8+10=5b−4b 8 + 10 = 5b - 4b 8+10=5b−4b 18=b 18 = b 18=bThe speed of the boat in still water is 18 km/h.

STEP 7

Now, calculate the distance using the downstream speed and time:Distance = (b+2)×4=(18+2)×4=20×4=80 (b + 2) \times 4 = (18 + 2) \times 4 = 20 \times 4 = 80 (b+2)×4=(18+2)×4=20×4=80 kmThe distance between the two docks is:80 \boxed{80} 80​ km

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. The motorboat travels downstream for 4 hours and upstream for 5 hours.
2. The speed of the river current is 2 km/h.
3. We need to find the distance between the two docks.

1. Define variables for the speeds.
2. Write expressions for the downstream and upstream speeds.
3. Use the time, speed, and distance relationship to form equations.
4. Solve the equations to find the distance.

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

Write expressions for the downstream and upstream speeds.
- Downstream speed = $b + 2$ km/h (since the current aids the boat's speed). - Upstream speed = $b - 2$ km/h (since the current opposes the boat's speed).

Solve the equation to find the speed of the boat in still water.
Expand both sides:
$4b + 8 = 5b - 10$
Rearrange to solve for $b$ :
$8 + 10 = 5b - 4b$ $18 = b$
The speed of the boat in still water is 18 km/h.

Now, calculate the distance using the downstream speed and time:
Distance = $(b + 2) \times 4 = (18 + 2) \times 4 = 20 \times 4 = 80$ km
The distance between the two docks is:
$\boxed{80}$ km