Question

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Answer 1

Answer:

The first plane's average rate = 560

Th equation used to solve is:

2.25x + 1.25(x-108) = 1825

Step-by-step explanation:

Sometimes the tests are picky with how you enter equations. The one above has proven to be correct in a test. It's a similar, but simplified version of the previous answer.

Answer 2

Answer:

(a) 1825 = 2.25x + (2.25-1)(x -108)

(b) 560 mi/h

Step-by-step explanation:

(a) distance = speed·time

The first plane's speed is x. The distance it travels in 2.25 hours is 2.25x.

The second plane's speed is x-108. It travels only 1.25 hours (since it started an hour later). The distance it travels is then (2.25 -1)(x -108).

The problem statement tells us the total of the distances traveled by the two planes is 1825 miles, so we can write the equation ...

... 1825 = 2.25x + (2.25 -1)(x -108)

(b) Simplifying the equation gives ...

... 1825 = 3.50x -135

To solve this 2-step equation, we add 135, then divide by 3.50.

.. 1960 = 3.50x

... 1960/3.50 = x = 560

The first airplane's speed is 560 mph.

Check

In 2.25 hours, the first plane travels (560 mi/h)·(2.25 h) = 1260 mi.

In 1.25 hours, the second plane travels (452 mi/h)·(1.25 h) = 565 mi.

Then 2.25 hours after the first plane leaves, the planes are 1260 +565 = 1825 miles apart, as given in the problem statement.