Math Problem Statement
A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:
4
5
6
10
Solution
Let the speed of the motorboat in still water be km/h. Let the speed of the stream be km/h. The total distance downstream and upstream is 30 km each, and the total time taken is 4 hours and 30 minutes, which is equivalent to hours.
Step 1: Calculate time taken for each part of the trip.
- Downstream speed = speed of motorboat + speed of stream = km/h.
- Upstream speed = speed of motorboat - speed of stream = km/h.
The time taken to go downstream is: The time taken to go upstream is:
Step 2: Set up the equation for total time.
The total time is the sum of the downstream and upstream times: Substituting the values:
Step 3: Solve the equation.
To solve this, first eliminate the fractions by finding a common denominator.
Let's solve it.from sympy import symbols, Eq, solve
Define the variable and equation
x = symbols('x')
Downstream and upstream time equations
downstream_time = 30 / (15 + x) upstream_time = 30 / (15 - x)
Total time equation
total_time_eq = Eq(downstream_time + upstream_time, 4.5)
Solve for x
speed_of_stream = solve(total_time_eq, x) speed_of_streamThe solution for the speed of the stream is km/h.
Since speed cannot be negative, the speed of the stream is km/h.
Would you like more details on the steps, or do you have any other questions?
Here are five related questions:
- What would the total time be if the stream's speed were 4 km/h?
- How would the problem change if the motorboat had a different speed?
- What if the distance downstream and upstream were unequal?
- How do currents affect real-world navigation for boats?
- What are other ways to solve similar riverboat problems?
Tip: When working with distance-rate-time problems, always ensure that the units are consistent across calculations.
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Math Problem Analysis
Mathematical Concepts
Speed, Distance, Time Problems
Relative Speed
Formulas
Time = Distance / Speed
Theorems
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Suitable Grade Level
Grades 9-12
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