A boat covers equal distances upstream and downstream in a total time of 5 hours. The sum of the boat’s speeds in upstream and downstream directions is 40 km/h. The speed of the boat in still water is 600% more than the speed of the stream. What is the approximate distance (in km) covered by the boat in the downstream direction?

Introduction / Context:
This is a multi-step boats and streams problem that combines ideas of upstream and downstream speeds, percentage comparison between boat speed and stream speed, and total travel time for equal distances. You are also asked to choose an approximate distance, so rounding to a nearby option is required after calculation.

Given Data / Assumptions:

• The boat travels an equal distance d km upstream and d km downstream.
• Total time for both journeys = 5 hours.
• Sum of upstream and downstream speeds = 40 km/h.
• The speed of the boat in still water is 600% more than the speed of the stream.
• Let b be the speed of the boat in still water (km/h).
• Let s be the speed of the stream (km/h).
• Upstream speed = b - s, downstream speed = b + s.

Concept / Approach:
First, use the given sum of upstream and downstream speeds to find the boat speed in still water. Then interpret “600% more” correctly to relate b and s. This allows us to find both b and s as numerical values. Finally, write the total time for equal distances upstream and downstream, use the known speeds and total time of 5 hours to solve for the distance d, and then choose the closest option.

Step-by-Step Solution:
Step 1: Upstream speed + downstream speed = (b - s) + (b + s) = 2b = 40 ⇒ b = 20 km/h. Step 2: “Speed of boat in still water is 600% more than speed of stream” means b = s + 600% of s = s + 6s = 7s. Step 3: From b = 7s and b = 20, we get 7s = 20 ⇒ s = 20 / 7 ≈ 2.857 km/h. Step 4: Upstream speed = b - s ≈ 20 - 2.857 ≈ 17.143 km/h. Step 5: Downstream speed = b + s ≈ 20 + 2.857 ≈ 22.857 km/h. Step 6: Time upstream = d / 17.143 hours; time downstream = d / 22.857 hours. Step 7: Total time = d / 17.143 + d / 22.857 = 5 hours. Step 8: Compute the sum of reciprocals: 1 / 17.143 + 1 / 22.857 ≈ 0.102083 per hour. Step 9: So d * 0.102083 ≈ 5 ⇒ d ≈ 5 / 0.102083 ≈ 48.96 km.

Verification / Alternative check:
If the downstream distance is about 49 km, the upstream time is roughly 49 / 17.143 ≈ 2.86 hours and the downstream time is about 49 / 22.857 ≈ 2.14 hours. The total is approximately 5 hours, agreeing with the question. Since the answer choices are rounded, 48.96 km is closest to 50 km.

Why Other Options Are Wrong:
Options 45 and 40 km would lead to total times noticeably less than 5 hours, while 55 and 60 km would give total times significantly greater than 5 hours. Only about 49–50 km keeps the total time near 5 hours with the calculated speeds, making 50 km the best approximate choice.

Common Pitfalls:
A frequent mistake is to misinterpret “600% more” as b = 6s instead of b = 7s. Another issue is forgetting that 2b equals the sum of upstream and downstream speeds. Finally, some learners try to avoid working with decimals and guess the distance without computing, which often leads to the wrong option. Working through the equations carefully and then rounding at the end is the safest method.

Final Answer:
The approximate distance covered by the boat in the downstream direction is 50 km.