A boat travels 30 km upstream and 30 km downstream in a total time of 6 hours. I
Practice Questions
Q1
A boat travels 30 km upstream and 30 km downstream in a total time of 6 hours. If the speed of the boat in still water is 10 km/h, what is the speed of the current?
2 km/h
3 km/h
4 km/h
5 km/h
Questions & Step-by-Step Solutions
A boat travels 30 km upstream and 30 km downstream in a total time of 6 hours. If the speed of the boat in still water is 10 km/h, what is the speed of the current?
Correct Answer: 2 km/h
Step 1: Understand that the boat travels upstream and downstream. Upstream means against the current, and downstream means with the current.
Step 2: Let the speed of the current be 'x' km/h.
Step 3: The speed of the boat in still water is given as 10 km/h.
Step 4: When the boat is going upstream, its effective speed is (10 - x) km/h because it is going against the current.
Step 5: When the boat is going downstream, its effective speed is (10 + x) km/h because it is going with the current.
Step 6: The time taken to travel upstream 30 km is calculated using the formula: time = distance / speed. So, time upstream = 30 / (10 - x).
Step 7: The time taken to travel downstream 30 km is calculated similarly: time downstream = 30 / (10 + x).
Step 8: The total time for both trips is given as 6 hours. So, we can write the equation: (30 / (10 - x)) + (30 / (10 + x)) = 6.
Step 9: To solve this equation, first find a common denominator and combine the fractions.
Step 10: After simplifying the equation, you will get a quadratic equation in terms of 'x'.
Step 11: Solve the quadratic equation to find the value of 'x'. You will find that x = 2 km/h.
Step 12: Therefore, the speed of the current is 2 km/h.
Relative Speed – Understanding how to calculate effective speeds when dealing with currents in water.
Time and Distance Relationship – Applying the formula time = distance/speed to find total travel time.
Algebraic Manipulation – Solving equations to find the unknown variable, in this case, the speed of the current.
