Question

Arun's swimming speed in still water is 5 km/hr. He swims between two points in a river and returns to the starting point. He took 20 minutes more upstream than downstream. If the stream speed is 2 km/hr, the distance between the points is:

• A. 3 km
• B. 1.5 km
• C. 1.75 km
• D. 1 km

Hint:

When dealing with problems involving speed, time, and distance, it’s important to set up equations based on the formula \( \text{Distance} = \text{Speed} \times \text{Time} \). For problems involving upstream and downstream travel, remember that the effective speed is altered by the speed of the stream. In this case, the upstream speed is reduced and the downstream speed is increased due to the current. Simplify the equation step by step to find the unknown distance, ensuring the units of time and speed match up correctly.

Answer 1

The Correct Option is C

We are given:

Speed in still water \(v = 5 \text{ km/hr}\),
Speed of stream \(u = 2 \text{ km/hr}\),
Additional time taken upstream = 20 minutes = \(\frac{1}{3}\) hours.

The effective speeds are:

Speed Upstream = \(v - u = 5 - 2 = 3 \text{ km/hr}\),
Speed Downstream = \(v + u = 5 + 2 = 7 \text{ km/hr}\).

Let the distance between the two points be \(d \text{ km}\). The time taken for upstream and downstream travel is:

Time Upstream = \(\frac{d}{3}\),
Time Downstream = \(\frac{d}{7}\).

The difference in time between upstream and downstream travel is:

\(\frac{d}{3} - \frac{d}{7} = \frac{1}{3}\).

Simplify the equation:

\(\frac{7d - 3d}{21} = \frac{1}{3}\),
\(\frac{4d}{21} = \frac{1}{3}\).

Multiply through by 21:

\(4d = 7\), \(d = \frac{7}{4} = 1.75 \text{ km}\).

Thus, the distance between the two points is 1.75 km.

Answer 2

We are given the following information:

Speed in still water \( v = 5 \text{ km/hr} \),
Speed of stream \( u = 2 \text{ km/hr} \),
Additional time taken upstream = 20 minutes = \( \frac{1}{3} \) hours.

Effective Speeds:

The effective speeds are calculated as follows:

Speed Upstream = \( v - u = 5 - 2 = 3 \text{ km/hr} \),
Speed Downstream = \( v + u = 5 + 2 = 7 \text{ km/hr} \).

Calculating the Distance Between the Two Points:

Let the distance between the two points be \( d \text{ km} \). The time taken for upstream and downstream travel is:

Time Upstream = \( \frac{d}{3} \),
Time Downstream = \( \frac{d}{7} \).

Time Difference:

The difference in time between upstream and downstream travel is:

\( \frac{d}{3} - \frac{d}{7} = \frac{1}{3} \).

Simplifying the Equation:

Now, simplify the equation to solve for \( d \):

\( \frac{7d - 3d}{21} = \frac{1}{3} \),
\( \frac{4d}{21} = \frac{1}{3} \).

Multiplying Through by 21:

To eliminate the denominator, multiply both sides by 21:

\( 4d = 7 \), so \( d = \frac{7}{4} = 1.75 \text{ km} \).

Conclusion:

The distance between the two points is \( 1.75 \) km.

Final Answer:

1.75 km