Question

A steamboat travels upstream, against the current, at a speed of 5 miles per hour. Later, the steamboat travels downstream with the current, at a speed of 9 miles per hour. Choose the system of equations that can be solved to find the speed of the steamboat, x, and the speed of the current, y.

a) x - y = 5
x + y = 9
b) x + y = 5
x - y = 9
c) x - 5y = 1
x + 9y = 1
d) x + 5y = 9
x - 9y = 5

Answer 1

The correct system of equations to determine the steamboat's speed in still water (x) and the current's speed (y) is x - y = 5 (upstream speed) and x + y = 9 (downstream speed).

Step-by-step explanation:

The speed of a steamboat and the current can be represented in a system of equations where x is the steamboat's speed in still water and y is the current's speed. When the steamboat is traveling upstream against the current, its effective speed is reduced by the speed of the current (x - y). Conversely, when traveling downstream, its effective speed is increased by the current's speed (x + y). Thus, the correct system of equations, given that upstream speed is 5 mph and downstream is 9 mph, is:

• x - y = 5
• x + y = 9

This system implies that in still water (x), the steamboat's original speed combined with the current (y), or against the current, will give the observed effective speeds in each direction.