Question 1111327: 1.The pilot of the Western Airlines flight from Los Angeles to
Honolulu announced en route that the plane was flying at a certain
airspeed with a west wind blowing at 30 mph. However, after flying
for 3 hours, the wind decreased to 20 mph (airspeed constant).
The plane arrived in Honolulu 2 hours later. If the distance from
Los Angeles to Honolulu is 2500 miles, what did the pilot
announce was the airspeed of the plane?
2.Hank and Hossein open a print shop. They receive a job which
Hank can do in 12 hours or Hossein in 14. They start to work on
it together, but after 3 hours, Hossein has to stop to finish another
job. Hank works alone for an hour, when he is called out on an estimate. Hossein come back and finishes the original job alone.
How long will it take him to finish?
3.A 4-inch-wide picture frame surrounds a picture 2 inches longer
than it is wide. If the area of the frame is 208 square inches, what
are the dimensions of the picture~ (Hint: Find the difference
between the area of the picture and the area formed by the
outside dimensions of the frame.)
4. Bud and Karen went fishing. At the end of the day they compared
catches. Together they had caught 40 fish. If Bud had caught two
more and Karen had caught two fewer, they would have caught the
same number of fish. What was the size of each catch~
5. Maggie and Rod left at 9 A.M. on a hike to Tahquitz peak, traveling
at an average rate of 2 mph, with three 5-minute rest stops. After a
45-minute lunch at the peak, they returned home averaging 3 mph
and arrived at 3 P.M. How long did it take them to reach the peak
and how far did they hike to reach it?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! For 1
distance=velocity*time or (x-30)3+(x-20)2=2500 if x is the speed of the plane
3x-90+2x-40=2500
5x=2630
x=526 mph, so 496 mph*3 hours (1488) and 506*2 hours (1012) miles.
At the time of the announcement, the airspeed was 496 mph. ANSWER.
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Hank works 4 hours total, Hossein works 3+x hours.
In one hour, Hank does (1/12) and Hossein does (1/14)
In 4 hours, Hank does 1/3 (4/12)
That means Hossein must do 2/3 of it and his share was (3+x)/14, where 3 was the hours worked and x the number of hours left.
(2/3)=(3+x)/14)
9+3x=28
3x=19
x=(19/3) hours or 6h20m
That is how much longer.
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The area of the whole thing ix (x+8)(x+10) (draw it)
That is x^2+18x+80
Subtract the area of the picture or x^2+2x to get 16x+80 which is the area of the frame.
so 16x+80=208
16x=128
x=8 inches
x+2=10 inches
Area of picture is 80 in^2 8 x 10 picture
Area of whole thing is 288 in ^2 16 x 18 whole thing.
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B+K=40
B+2=K-2
K=B+4
B+4+B=40
2B=36
B=18 Bud
K=22 Karen
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distance=velocity * time
Coming downhill was 3mph* x hours
The total time hiking for uphill must be 5-x, the 5 being 6 hours minus 45 minutes for lunch and 3 5 minute breaks
uphill was 2 mph*(5-x)
distances up and down are equal
3x=2(5-x)
3x=10-2x
5x=10
x=2 hours
That is hiking time, so distance down was 6 miles
Distance up is 2(5-2) or 6 miles.
It took 2 hours down, 45 minutes for lunch, so it took them 3 hours and 15 minutes to get to the top, hiking at an average speed of 2 mph and with 3 5 minute breaks.
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