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Math  /  Algebra

QuestionSeconds to tad 200 km dan the arar. \qquad
2. A river flows north with a current of 4.0 meters per second. a. If it takes a motor boat 7.0 minutes to travel 1.5 km
Part A upstream (against the current), at what speed can the motor whet suedat push the boat through the water? 7 min+1 s2 mm7 \mathrm{~min}+1 \mathrm{~s}^{2} \mathrm{~mm} b. How long will it take the boat to travel 2 km ? GG G:G: n！ E:
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Studdy Solution

STEP 1

1. The river flows north with a current speed of 4.0 meters per second.
2. The motorboat takes 7.0 minutes to travel 1.5 km upstream.
3. We need to find the speed of the motorboat in still water.
4. We need to find the time it takes for the boat to travel 2 km downstream.

STEP 2

1. Convert units for consistency.
2. Calculate the speed of the motorboat in still water.
3. Calculate the time taken to travel downstream.

STEP 3

Convert the time from minutes to seconds for consistency in units: 7.0 minutes=7.0×60=420 seconds 7.0 \text{ minutes} = 7.0 \times 60 = 420 \text{ seconds}
Convert the distance from kilometers to meters: 1.5 km=1.5×1000=1500 meters 1.5 \text{ km} = 1.5 \times 1000 = 1500 \text{ meters}

STEP 4

Let v v be the speed of the motorboat in still water in meters per second.
The effective speed upstream is v−4.0 v - 4.0 meters per second.
Using the formula for speed, speed=distancetime \text{speed} = \frac{\text{distance}}{\text{time}} , we have: v−4.0=1500420 v - 4.0 = \frac{1500}{420}
Solve for v v : v−4.0=1500420≈3.57 v - 4.0 = \frac{1500}{420} \approx 3.57
v=3.57+4.0=7.57 meters per second v = 3.57 + 4.0 = 7.57 \text{ meters per second}

STEP 5

For downstream travel, the effective speed is v+4.0 v + 4.0 .
The distance to travel downstream is 2 km, which is: 2 km=2000 meters 2 \text{ km} = 2000 \text{ meters}
Calculate the time taken using the formula time=distancespeed \text{time} = \frac{\text{distance}}{\text{speed}} : time=20007.57+4.0 \text{time} = \frac{2000}{7.57 + 4.0}
time=200011.57≈172.85 seconds \text{time} = \frac{2000}{11.57} \approx 172.85 \text{ seconds}
Convert time back to minutes if needed: 172.85 seconds≈2.88 minutes 172.85 \text{ seconds} \approx 2.88 \text{ minutes}
The speed of the motorboat in still water is 7.57 meters per second 7.57 \text{ meters per second} , and the time to travel 2 km downstream is approximately 2.88 minutes 2.88 \text{ minutes} .

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