The ratio of speed of a boat in downstream and speed of boat in upstream is 9:1. If the speed of current is 4 kmph, then find the distance travelled by the boat upstreams in 5 hours. 

Let the speed of the boat in still water be \( B \) km/h, and the speed of the current is given as \( C = 4 \) km/h.

We are given that the ratio of the speed of the boat downstream to the speed of the boat upstream is 9:1. 

### Step 1: Express the downstream and upstream speeds
- **Downstream speed** (boat moves with the current): \( B + C = B + 4 \) km/h.
- **Upstream speed** (boat moves against the current): \( B - C = B - 4 \) km/h.

From the problem, we know the ratio of downstream speed to upstream speed is 9:1:
\[
\frac{B + 4}{B - 4} = 9.
\]

### Step 2: Solve for \( B \)
To solve for \( B \), we cross multiply:
\[
B + 4 = 9(B - 4).
\]
Expanding both sides:
\[
B + 4 = 9B - 36.
\]
Now, bring all terms involving \( B \) to one side:
\[
4 + 36 = 9B - B,
\]
\[
40 = 8B.
\]
Solve for \( B \):
\[
B = \frac{40}{8} = 5 \text{ km/h}.
\]

### Step 3: Find the upstream speed
The upstream speed is \( B - C = 5 - 4 = 1 \text{ km/h} \).

### Step 4: Calculate the distance travelled upstream in 5 hours
The distance travelled upstream is given by:
\[
\text{Distance} = \text{Speed} \times \text{Time}.
\]
With a speed of \( 1 \) km/h and a time of \( 5 \) hours, the distance is:
\[
\text{Distance} = 1 \times 5 = 5 \text{ km}.
\]

Thus, the boat travels **5 km** upstream in 5 hours.

Would you like a detailed breakdown of any specific step?

Here are 5 related questions:
1. How would the solution change if the speed of the current was 6 km/h?
2. What would happen if the ratio of downstream to upstream speed was 8:1 instead of 9:1?
3. How can you derive the speed of the boat if the total journey (upstream and downstream) took 10 hours?
4. What is the formula for calculating the downstream speed given the current speed and boat speed in still water?
5. How can you apply this concept to a situation with varying current speeds?

**Tip:** Always check if the units for speed and time are consistent when solving distance-related problems!

The ratio of speed of a boat in downstream and speed of boat in upstream is 9:1. If the speed of current is 4 kmph, then find the distance travelled by the boat upstream in 5 hours.

Learn how to calculate the distance a boat travels upstream in 5 hours when the ratio of downstream to upstream speed is 9:1, and the current speed is 4 km/h. This problem explores key concepts such as speed, distance, time, and ratio. Suitable for Grades 8-10.

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