Difficulty: Easy
Correct Answer: 6 km/hr
Explanation:
Introduction / Context:
This question provides the effective speeds of a boat while travelling downstream and upstream and asks for the speed of the boat in still water. In boats and streams problems, the downstream speed is increased by the current, while the upstream speed is reduced by it. Knowing both effective speeds lets us compute both the boat speed in still water and the current speed.
Given Data / Assumptions:
Concept / Approach:
From the two equations b + c = 8 and b - c = 4, we can solve for b and c. The standard formulas are:
b = (downstream speed + upstream speed) / 2
c = (downstream speed - upstream speed) / 2
So we simply substitute the given numerical values and compute b. The distances are not needed because the speeds already reflect the effect of the current.
Step-by-Step Solution:
Step 1: Write the system of equations.
b + c = 8.
b - c = 4.
Step 2: Add the equations to eliminate c.
(b + c) + (b - c) = 8 + 4.
2b = 12.
b = 12 / 2 = 6 km/h.
Step 3: If needed, compute current speed.
From b + c = 8, c = 8 - 6 = 2 km/h.
Verification / Alternative check:
With b = 6 and c = 2, downstream speed is 6 + 2 = 8 km/h, matching the given value.
Upstream speed is 6 - 2 = 4 km/h, again matching the given value.
This confirms that b = 6 km/h is correct.
Why Other Options Are Wrong:
If b were 4.5, 5, 6.4 or 7 km/h, it would be impossible to choose a single current speed c such that b + c = 8 and b - c = 4 simultaneously.
Checking each option quickly shows contradictions in at least one of the equations.
Common Pitfalls:
One common error is to average 8 and 4 incorrectly or to forget that the boat speed is the midpoint between the downstream and upstream speeds.
Another pitfall is to mistake the current speed for the boat speed in still water and report c instead of b.
Final Answer:
The speed of the boat in still water is 6 km/hr.
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