Question

Boat moves 13 mph in water without current goes 133 miles upstream and 133 miles back again in 26 hours find the speed of the current?

Answer 1

To find the speed of the current, we can set up an equation using relative velocity. By simplifying the equation and solving for c, we find that the speed of the current is approximately 5.94 mph.

Step-by-step explanation:

To find the speed of the current, we can use the concept of relative velocity. Let's assume that the speed of the current is 'c' mph. When the boat is going upstream, its effective velocity will be the difference between its own speed and the speed of the current. So, the effective velocity will be (13 - c) mph. Therefore, the time taken to cover 133 miles upstream will be 133 / (13 - c) hours. Similarly, when the boat is going downstream, its effective velocity will be the sum of its own speed and the speed of the current. So, the effective velocity will be (13 + c) mph. Therefore, the time taken to cover 133 miles downstream will be 133 / (13 + c) hours. Since the total time taken for the round trip is given as 26 hours, we can set up the equation: 133 / (13 - c) + 133 / (13 + c) = 26.

To solve this equation, we can first simplify it by finding a common denominator:

• [(133)(13 + c) + (133)(13 - c)] / [(13 - c)(13 + c)] = 26

After simplifying, we get:

• [(133)(26)] / [(169 - c^2)] = 26

We can then cross multiply and solve for c^2:

• (133)(26) = 26(169 - c^2)

By simplifying further, we get:

• 3468 = 4384 - 26c^2

After rearranging the equation, it becomes:

• 26c^2 = 916

Finally, we solve for c:

• c^2 = 35.23
• c ≈ 5.94

Therefore, the speed of the current is approximately 5.94 mph.