QuestionJane took 10 min upstream and 5 min downstream. If the current is $6 \mathrm{~km}$ /hr, find her boat speed in still water.

Studdy Solution

STEP 1

Assumptions1. The time taken to drive the boat upstream is10 minutes. The time taken to drive the boat downstream is5 minutes3. The speed of the current is6 km/hr4. The speed of the boat in still water is the same in both directions5. The distance traveled upstream and downstream is the same

STEP 2

First, we need to convert the time from minutes to hours since the speed of the current is given in km/hr.
$Time_{upstream} =10\, min = \frac{10}{60}\, hr$ $Time_{downstream} =5\, min = \frac{5}{60}\, hr$

STEP 3

Let's denote the speed of the boat in still water as $v$ (in km/hr). Then the speed of the boat upstream (against the current) is $v -6$ km/hr, and the speed downstream (with the current) is $v +6$ km/hr.

STEP 4

The distance traveled is the same in both directions. We can express the distance as the product of time and speed. So, we have the following equation $Time_{upstream} \times Speed_{upstream} = Time_{downstream} \times Speed_{downstream}$

STEP 5

Substitute the expressions for the times and speeds into the equation $\frac{10}{60} \times (v -) = \frac{5}{60} \times (v +)$

STEP 6

implify the equation by multiplying both sides by60 to get rid of the fractions $10 \times (v -6) =5 \times (v +6)$

STEP 7

Expand both sides of the equation $10v -60 =5v +30$

STEP 8

Rearrange the equation to isolate $v$ $10v -5v =60 +30$

STEP 9

implify the equation $5v =90$

STEP 10

olve for $v$ $v = \frac{90}{5} =18$ Jane's boat speed in still water was18 km/hr.

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