Question

On A riverboat traveled 10 miles upstream against the

current in 5 hours. The return trip took only half
da
the amount of time while the boat traveled with the current.

a. Write an equation for the trip upstream.
b. Write an equation for the return trip.
c. Use combination/elimination to find the speed of the boat and the speed of the current.

Answer 1

a. Let x be the speed of the boat in miles per hour and y be the speed of the current in miles per hour. Since the boat traveled upstream, the speed of the current is added to the speed of the boat. Therefore, the equation for the trip upstream is:

distance = (x + y) * time

10 = (x + y) * 5

b. For the return trip, the speed of the current is subtracted from the speed of the boat. Therefore, the equation for the return trip is:

distance = (x - y) * (time/2)

10 = (x - y) * (5/2)

c. To find the speed of the boat and the speed of the current, we can use the method of elimination. From the first equation, we have:

10 = 5x + 5y

From the second equation, we have:

10 = 2.5x - 2.5y

Now we can use the elimination method by multiplying the first equation by 2 and then subtracting the second equation from it.

20 = 10x + 10y

20 = 5x - 5y

so we have

0 = 5x + 5y - 5x + 5y

0 = 10y

The equation becomes impossible to solve as we can't divide by 0.

As we know that the speed of the boat and the speed of the current are non-zero numbers, we can't find the exact speed of the boat and the current. We can conclude that the information given is not sufficient to find the exact speed of the boat and the current.

Explanation: