SOLUTION: A battleship started at 7:00 AM on a 500 mile voyage on a special mission but was brought to a full stop an hour after starting for military reasons, delaying it for a full hour, a

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Question 695260: A battleship started at 7:00 AM on a 500 mile voyage on a special mission but was brought to a full stop an hour after starting for military reasons, delaying it for a full hour, after which it was ordered to proceed at a reduced velocity equivalent to 75% of its original speed. This ship arrived at its destination 3 ¾ hr. after the scheduled time. Determine the original speed of the battleship.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A battleship started at 7:00 AM on a 500 mile voyage on a special mission
but was brought to a full stop an hour after starting for military reasons,
delaying it for a full hour, after which it was ordered to proceed at a reduced
velocity equivalent to 75% of its original speed.
This ship arrived at its destination 3 ¾ hr. after the scheduled time.
Determine the original speed of the battleship.
:
Let s = original speed of the ship
:
change 33%2F4 to 3.75 hrs
:
500%2Fs = time of voyage with no stops or change in speed
:
Write a distance equation of the actual voyage
:
dist at normal speed + distance at reduced speed = 500 mi
1s + .75s(500%2Fs - 1 + 3.75) = 500
1s + .75s(500%2Fs + 2.75) = 500
1s + (.75s(500%2Fs) + .75s(2.75) = 500
1s + 375 + 2.0625s = 500
3.0625s = 500 - 375
3.0625s = 125
s = 125/3.0625
s = 40.8 mph (or knots if nautical miles are used)
:
:
See if that checks out
normal time: 500/40.8 = 12.25 hrs
Additional time required 3.75 hrs
------------------------------------
Actual time of the voyage: 16 hrs
:
(500-40.8) = 459.2 mi at 3/4 speed which is .75(40.8) = 30.6 knots
459.2%2F30.6 = 15 hr + 1 hr at normal speed = 16 hrs, the actual time