Calculating Downstream Boat Speed

This question involves concepts related to boat and stream speeds. We are given the speed of the boat when it moves against the stream (upstream speed) and its speed in still water. We need to find its speed when it moves along the stream (downstream speed).

Understanding Boat and Stream Concepts

• Speed in Still Water (B): The speed of the boat without any influence from the stream.
• Speed of Stream (S): The speed at which the water is flowing.
• Upstream Speed (U): The speed of the boat when it moves against the stream. The stream resists the boat's movement, so Upstream Speed = Speed in Still Water - Speed of Stream ($\text{U} = \text{B} - \text{S}$).
• Downstream Speed (D): The speed of the boat when it moves with the stream. The stream helps the boat's movement, so Downstream Speed = Speed in Still Water + Speed of Stream ($\text{D} = \text{B} + \text{S}$).

Applying the Formulas to Find Downstream Speed

We are given:

• Upstream Speed ($\text{U}$) = 40 km/hr
• Speed in Still Water ($\text{B}$) = 55 km/hr

We need to find the Downstream Speed ($\text{D}$).

Step 1: Find the Speed of the Stream (S)

We know that Upstream Speed ($\text{U}$) is the difference between the speed in still water ($\text{B}$) and the speed of the stream ($\text{S}$).

The formula is: $\text{U} = \text{B} - \text{S}$

Substitute the given values:

40 = 55 - S

Now, we solve for S:

S = 55 - 40

S = 15 km/hr

So, the speed of the stream is 15 km/hr.

Step 2: Find the Downstream Speed (D)

We know that Downstream Speed ($\text{D}$) is the sum of the speed in still water ($\text{B}$) and the speed of the stream ($\text{S}$).

The formula is: $\text{D} = \text{B} + \text{S}$

Substitute the known values (B = 55 km/hr and S = 15 km/hr):

D = 55 + 15

D = 70 km/hr

Thus, the downstream speed of the boat is 70 km/hr.

Conclusion

Based on the calculations, the downstream speed of the boat is 70 km/hr.

Revision Table: Boat and Stream Formulas

Additional Information: Related Concepts

Boat and stream problems are a common type in quantitative aptitude. They test the understanding of relative speeds. Here are some key points:

• When moving downstream, the stream's speed is added to the boat's speed in still water, resulting in a higher effective speed.
• When moving upstream, the stream's speed is subtracted from the boat's speed in still water, resulting in a lower effective speed.
• If you are given the upstream and downstream speeds, you can find the speed in still water and the speed of the stream using the formulas provided in the revision table.
• These concepts are applications of relative speed principles, where the speed of one object is considered relative to another.