Jane took 

20

min to drive her boat upstream to​ water-ski at her favorite spot. Coming back later in the​ day, at the same boat​ speed, took her 

10

min. If the current in that part of the river is 

9

km per​ hr, what was her boat speed in still​ water?

Let the boat speed in still water be \( v_b \) (in km/h), and let the speed of the current be \( v_c = 9 \, \text{km/h} \).

When Jane is driving upstream, her effective speed is \( v_b - v_c \), and when she is driving downstream, her effective speed is \( v_b + v_c \).

We know that:
- Time taken to go upstream is 20 minutes = \( \frac{1}{3} \) hours.
- Time taken to go downstream is 10 minutes = \( \frac{1}{6} \) hours.

Let the distance to her favorite spot be \( d \) km. Using the relationship \( \text{distance} = \text{speed} \times \text{time} \), we can write two equations:

1. For upstream:
\[
d = \left( v_b - 9 \right) \times \frac{1}{3}
\]

2. For downstream:
\[
d = \left( v_b + 9 \right) \times \frac{1}{6}
\]

Since both distances are equal, we can set the two equations equal to each other:

\[
\left( v_b - 9 \right) \times \frac{1}{3} = \left( v_b + 9 \right) \times \frac{1}{6}
\]

Now we can solve for \( v_b \), the boat speed in still water.

### Step 1: Solve the equation

\[
\frac{v_b - 9}{3} = \frac{v_b + 9}{6}
\]

Multiply both sides by 6 to eliminate the fractions:

\[
2(v_b - 9) = v_b + 9
\]

Expand both sides:

\[
2v_b - 18 = v_b + 9
\]

### Step 2: Isolate \( v_b \)

\[
2v_b - v_b = 9 + 18
\]

\[
v_b = 27 \, \text{km/h}
\]

Thus, the boat speed in still water is \( 27 \, \text{km/h} \).

Would you like further details or clarification on any step?

### Related Questions:
1. What would Jane's total travel time be for a 15 km round trip at this boat speed?
2. How would the travel times change if the current speed increased to 12 km/h?
3. What would be the downstream time if her boat speed increased by 5 km/h?
4. How far could Jane travel upstream in 40 minutes at her current boat speed?
5. What happens if the current is faster than the boat's speed in still water?

### Tip:
Always convert time units consistently to either hours or minutes to avoid calculation errors when working with speed problems!

Jane took 20 min to drive her boat upstream to water-ski at her favorite spot. Coming back later in the day, at the same boat speed, took her 10 min. If the current in that part of the river is 9 km per hr, what was her boat speed in still water?

Calculate the boat speed in still water when Jane takes 20 minutes to go upstream and 10 minutes to return downstream with a river current of 9 km/h. This problem covers speed, distance, and time equations suitable for Grades 9-10.

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