A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream

A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream

To solve the problem of finding the time taken by a boat to travel 68 km downstream, given the boat's speed in still water and the speed of the stream, follow these steps.

Speed of the Boat in Still Water: 13 km/hr

Speed of the Stream: 4 km/hr

Distance to be Traveled Downstream: 68 km

Calculate the Speed Downstream:

When traveling downstream, the speed of the boat is the sum of its speed in still water and the speed of the stream.

Speed downstream = Speed of the boat in still water + Speed of the stream

Therefore, Speed downstream = 13 km/hr + 4 km/hr = 17 km/hr

Calculate the Time Taken:

Time is calculated by dividing the distance by the speed.

Time taken = Distance / Speed downstream

Therefore, Time taken = 68 km / 17 km/hr

Simplify the division to find the time.

Time taken = 68 / 17 = 4 hours

The boat takes 4 hours to travel 68 km downstream.

How to Calculate Time for Boat and Stream problems?

Boat and stream problems are common in mathematics, especially in algebra and physics. These problems involve calculating the effective speed of a boat when it is traveling in still water versus when it is moving with or against the current of a stream. Understanding these concepts is essential for solving related problems efficiently.

Speed in Still Water:

This is the speed of the boat when the water is not moving. It is often given as a constant value.

Speed of the Stream:

The speed at which the water in the stream is flowing. This affects the overall speed of the boat when it is moving downstream (with the current) or upstream (against the current).

Downstream Speed:

When a boat travels downstream, its effective speed increases because the speed of the stream is added to the boat's speed in still water.

Downstream speed = Speed in still water + Speed of the stream

Upstream Speed:

When a boat travels upstream, its effective speed decreases because the speed of the stream is subtracted from the boat's speed in still water.

Upstream speed = Speed in still water - Speed of the stream

Time Calculation:

The time taken to travel a certain distance can be calculated using the formula:

Time = Distance / Speed

Key Points

• Determine the speed of the boat in still water and the speed of the stream.
• Note the distance that needs to be traveled either upstream or downstream.
• Use the appropriate formula to calculate the effective speed of the boat when moving upstream or downstream.
• Use the time formula to find out how long it will take for the boat to cover the given distance.
• Check the calculations to ensure that they make sense and the units are consistent.