A boat's crew rowed 7.5 miles downstream, with the current, in 1.5 hours. the return trip upstream, against the current, covered the same distance, but took 2.5 hours. find the crew's average rowing velocity in still water and the average velocity of the current.

Average rowing velocity of boat in still water is 4 miles per hour and average velocity of the current is 1 mile per hour.

Step-by-step explanation:

We are given the following in the question:

Let x be the average rowing velocity of boat in still water and y be the the average velocity of the current.

The boat rowed 7.5 miles downstream, with the current, in 1.5 hours.

Velocity with the current =

Thus, we can write the equation:

The return trip upstream, against the current, covered the same distance, but took 2.5 hours.

Velocity against the current =

Thus, we can write the equation:

Solving, the two equations:

Thus, average rowing velocity of boat in still water is 4 miles per hour and average velocity of the current is 1 mile per hour.

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step-by-step explanation:

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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