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.
<u>Check</u>
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.
