The total distance travelled by a boat 1 hour upstream and 30 minutes downstream in which the rate of current is 3 kph

To solve the problem, we need to calculate the total distance traveled by the boat upstream and downstream, taking into account the speed of the current.

Let's denote:
- \( v_b \) as the speed of the boat in still water (in kph).
- \( v_c = 3 \) kph as the speed of the current.

### Upstream:
When traveling upstream, the effective speed of the boat is reduced by the speed of the current. The effective speed upstream \( v_{up} \) is:
\[
v_{up} = v_b - v_c = v_b - 3 \text{ kph}
\]
The boat travels for 1 hour upstream, so the distance traveled upstream \( d_{up} \) is:
\[
d_{up} = v_{up} \times 1 = (v_b - 3) \times 1 = v_b - 3 \text{ km}
\]

### Downstream:
When traveling downstream, the effective speed of the boat is increased by the speed of the current. The effective speed downstream \( v_{down} \) is:
\[
v_{down} = v_b + v_c = v_b + 3 \text{ kph}
\]
The boat travels for 30 minutes (which is \( 0.5 \) hours) downstream, so the distance traveled downstream \( d_{down} \) is:
\[
d_{down} = v_{down} \times 0.5 = (v_b + 3) \times 0.5 = 0.5v_b + 1.5 \text{ km}
\]

### Total Distance:
The total distance \( d_{total} \) traveled by the boat is the sum of the upstream and downstream distances:
\[
d_{total} = d_{up} + d_{down} = (v_b - 3) + (0.5v_b + 1.5) = 1.5v_b - 1.5 \text{ km}
\]

So, the total distance traveled by the boat is \( 1.5v_b - 1.5 \) kilometers, where \( v_b \) is the speed of the boat in still water.

If you have the value of \( v_b \) (the speed of the boat in still water), you can plug it into the equation to get the exact total distance.

Would you like to provide the boat's speed or have any more questions?

Here are 5 related questions:

1. How would the total distance change if the current's speed increased to 5 kph?
2. What if the boat traveled for 2 hours upstream and 1 hour downstream instead?
3. How does the speed of the current affect the time taken to travel a fixed distance upstream?
4. How would you calculate the total time taken for a round trip upstream and downstream over the same distance?
5. What if the boat had to travel against the current for the entire journey?

**Tip:** When dealing with current-related problems, always separate the calculations for upstream and downstream to account for the effect of the current correctly.

Learn how to calculate the total distance traveled by a boat when moving upstream and downstream with a current speed of 3 kph. Understand the effects of current on boat speed and distance over specified time periods. Suitable for Grades 9-12.

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