Difficulty: Easy
Correct Answer: 13 kmph
Explanation:
Introduction / Context:
Here we are given the time taken by a boat to travel a known distance upstream and the speed of the stream. From this information, we can compute the upstream speed and then determine the speed of the boat in still water. This is a straightforward application of the relationships between upstream speed, boat speed, and current speed.
Given Data / Assumptions:
Concept / Approach:
First we convert the time from minutes to hours, because speeds are given in km/h. Using distance and time, we compute the upstream speed. Since upstream speed equals b - c, where c is known, we can rearrange to get b. This is a direct and common pattern in boats and streams questions.
Step-by-Step Solution:
Step 1: Convert time from minutes to hours.
Time upstream = 42 minutes = 42 / 60 hours = 0.7 hours.
Step 2: Compute the upstream speed using speed = distance / time.
Upstream speed = 7 / 0.7 = 10 km/h.
Step 3: Use the upstream relationship b - c = upstream speed.
b - 3 = 10.
Step 4: Solve for b.
b = 10 + 3 = 13 km/h.
Verification / Alternative check:
With b = 13 km/h and c = 3 km/h, upstream speed becomes 13 - 3 = 10 km/h.
Time to cover 7 km upstream = 7 / 10 hours = 0.7 hours = 42 minutes, which matches the original information.
This confirms that b = 13 km/h is correct.
Why Other Options Are Wrong:
If b were 12 or 11 km/h, upstream speeds would be 9 or 8 km/h respectively, leading to times of 7 / 9 or 7 / 8 hours, which do not equal 42 minutes.
Values such as 14 or 10 km/h would produce upstream speeds that also do not lead to the given time of 42 minutes.
Common Pitfalls:
A common mistake is to forget to convert minutes into hours, resulting in an incorrect upstream speed.
Another is to misinterpret the 3 km/h as the upstream speed rather than the current speed, which leads to an incorrect equation.
Final Answer:
The speed of the boat in still water is 13 kmph.
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