A boat covers 63 km upstream in 9 hours and the same distance downstream in 7 hours. What is the speed (in km/h) of the boat in still water?

Introduction / Context:
This problem tests your understanding of upstream and downstream speeds and how to extract the boat's own speed from them. Instead of being given the speeds directly, you are given distance and time, so you must compute the effective speeds first.

Given Data / Assumptions:
• Distance each way = 63 km.• Time upstream = 9 hours.• Time downstream = 7 hours.• Let boat speed in still water be u km/h.• Let stream speed be v km/h.

Concept / Approach:
Speed = distance ÷ time. So we first compute the upstream and downstream speeds from the given distances and times. For boats-and-streams questions: upstream speed = u − v, downstream speed = u + v. Once we know those two values, we can find u as the average of them.

Step-by-Step Solution:
Step 1: Upstream speed = 63 ÷ 9 = 7 km/h.Step 2: Downstream speed = 63 ÷ 7 = 9 km/h.Step 3: Set up equations: u − v = 7 and u + v = 9.Step 4: Add the equations: (u − v) + (u + v) = 7 + 9.Step 5: This gives 2u = 16 ⇒ u = 16 ÷ 2 = 8 km/h.

Verification / Alternative check:
If u = 8 and upstream speed is 7, then v = u − 7 = 1 km/h. Check downstream: u + v = 8 + 1 = 9 km/h, which matches the found downstream speed. So our value of u is consistent.

Why Other Options Are Wrong:
7: This is the upstream speed, not the still-water speed.8.5 or 8.7: These values do not produce upstream and downstream speeds of exactly 7 and 9 when combined with a single current speed.

Common Pitfalls:
Many students try to average the times instead of speeds or forget to compute speeds before applying formulas. Always convert distance–time information into speeds first, then use the standard upstream/downstream relations.

Final Answer:
The speed of the boat in still water is 8 km/h.