A boat moves at 20 km/h in still water. The stream speed is x km/h. It takes 4 hours to travel 48 km downstream and 32 km upstream in total. What is x?

4

The governing concept is forming a rational equation from speed, distance, and time. Downstream speed is 20+x and upstream speed is 20-x, with 0<x<20. Therefore the total-time equation is 48/(20+x)+32/(20-x)=4. Testing x=4 gives 48/24+32/16=2+2=4, so option A satisfies the conditions. For completeness, clearing denominators gives 48(20-x)+32(20+x)=4(400-x^2), which simplifies to x^2-4x-80=0, so x=10 or x=-8; wait, this indicates the stated numerical data do not support x=4. Direct substitution confirms that x=4 works only because 48/24+32/16=4, while the cleared equation calculation must be expanded carefully: 1600-16x=1600-4x^2, hence x(x-4)=0. The positive stream speed is x=4. Distractors do not satisfy the total-time equation.

This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.