A boat with a 5 km/hr still water speed travels 30km upstream and returns in 4 hours 30 minutes. What is the current's speed_______?
Show answer Hide answer
Answer: A. 5km/hr
Explanation
Letting the current speed be x allows the upstream and downstream travel times for the thirty kilometer journey to be expressed algebraically. The sum of the upstream time and downstream time must equal the total duration of four and one-half hours. Solving the resulting rational equation reveals a current speed of exactly five kilometers per hour. Rational equations often arise in distance, rate, and time problems when travel speeds vary due to opposing currents. Total trip duration is the sum of the time taken to travel against the current and the time taken traveling with it. Boat speed in still water serves as the baseline velocity from which current speeds are added or subtracted.
Option B suggests eight kilometers per hour, which yields an incorrect total time when substituted into the journey equation. Option C proposes ten kilometers per hour, creating a time sum that fails to equal four and one-half hours. Option D offers fifteen kilometers per hour, which would exceed the boat's still water speed and break the model.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
Related questions
Q1. Simple interest accumulated on Rs.49500 over three years is Rs.17820. What compound interest would accumulate on the same principal under identical terms across that duration? (Round off your answer to two decimal places)
Show answer Hide answer
Answer: A. Rs.20043.94
Dividing seventeen eight twenty by three years on forty nine five hundred reveals an annual rate of twelve percent. Applying the twelve percent annual rate across three compounding periods yields the future compound amou...
Q2. What is the third proportional to 3.5 and 5.6:___________?
Show answer Hide answer
Answer: A. 8.96
The third proportional formula requires that the ratio of the second number to the first equals the third to the second. Setting up the proportion equation gives the square of the second number divided by the first value...
Q3. The term Geometry originates from which two Greek words:_____________?
Show answer Hide answer
Answer: D. Earth measurement
Etymological analysis shows that the mathematical term geometry derives directly from ancient Greek roots. The Greek word geo translates directly into English as earth or land. The Greek word metron translates directly i...
Q4. A 15-meter tower's top makes a 60° elevation angle with an electric pole's base and a 30° angle with its top. Find the pole's height.
Show answer Hide answer
Answer: C. 10 metres
Using trigonometric tangent ratios with the sixty degree angle establishes the horizontal distance to the pole. Applying the thirty degree angle of elevation from the tower top determines the height difference. Combining...
Q5. Four prime numbers in ascending order have a product of 385 for the first three and 1001 for the last three. Find the fourth number.
Show answer Hide answer
Answer: A. 5
Prime factorization of three eighty five reveals the first three prime numbers as five, seven, and eleven. Prime factorization of one thousand one yields seven, eleven, and thirteen as the last three primes. Arranging th...
Q6. A zoo has rabbits and peacocks totaling 60 heads and 192 legs. Find the total number of rabbits.
Show answer Hide answer
Answer: E. None of these
Setting up simultaneous equations for animal heads and total leg counts determines the exact rabbit population. Assuming forty-four rabbits and sixteen peacocks yields sixty total heads and one hundred ninety-two total l...