two speedboats leave the same dock at the same time and travel in exactly opposite directions. One boat is traveling 14 mph faster than the other boat. In half an hour the boats are 48 miles apart. Find the rate of the faster boat.

Let x = rate of slower boat

Let y = rate of faster boat

y = x + 14

time = 1/2 hr

then,

1/2x + 1/2y = 48

substitute for y

1/2x + 1/2(x+14) = 48

1/2x + 1/2x + 7 = 48

x = 41

y = 41 + 14 = 55 mph

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