A boat takes 3 hours more to travel 48 km upstream than to travel the same distance downstream. The speed of the stream is 4 km/h. What is the speed of the boat in still water?
Answer and explanation
Correct answer: 12 km/h
Let the speed of the boat in still water be \(x\) km/h. Its upstream and downstream speeds are then \(x-4\) and \(x+4\) km/h, respectively. Therefore, \(\frac{48}{x-4}-\frac{48}{x+4}=3\). On simplifying, we get \(x^2=144\), so \(x=12\) or \(x=-12\). Since speed is positive and must exceed the stream speed, the valid answer is 12 km/h. Exam tip: In boat-and-stream problems, use \(x-v\) for upstream speed and \(x+v\) for downstream speed.
Frequently asked questions
What is the correct answer to this question?
12 km/h
Why is this the correct answer?
Let the speed of the boat in still water be \(x\) km/h. Its upstream and downstream speeds are then \(x-4\) and \(x+4\) km/h, respectively. Therefore, \(\frac{48}{x-4}-\frac{48}{x+4}=3\). On simplifying, we get \(x^2=144\), so \(x=12\) or \(x=-12\). Since speed is positive and must exceed the stream speed, the valid answer is 12 km/h. Exam tip: In boat-and-stream problems, use \(x-v\) for upstream speed and \(x+v\) for downstream speed.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
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