SOLUTION: 1. Suppose you have a blue candle that is 8 feet tall and takes 10 hours to burn and a red candle that is 10 feet tall and takes 8 hours to burn. If you light them both at the dame

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Question 85897: 1. Suppose you have a blue candle that is 8 feet tall and takes 10 hours to burn and a red candle that is 10 feet tall and takes 8 hours to burn. If you light them both at the dame time, when (to the nearest minute) will the blue candle be 3 times the height of the red candle?
2. A bicycle wheel has a 12-inch radius. If you peddle at a rate of 60 revolutions per minute, how long will it take you to go 9 miles?
3. A luxury cruise ship leaves New York on its way to London. When it is 180 miles from shore a helicopter is sent out to catch up with the ship. The helicopter's spees is ten times that of the ship. Hwo far from New York does the helicopter catch up with the ship?
4. Meghan travels from A to B at 2 muntes per mile and returns over the same route at 2 miles per minute. Find her average speed, in miles per hour, for the whole trip.

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
1. Suppose you have a blue candle that is 8 feet tall and takes 10 hours to burn and a red candle that is 10 feet tall and takes 8 hours to burn. If you light them both at the dame time, when (to the nearest minute) will the blue candle be 3 times the height of the red candle?
:
Blue candle burn rate 8/10 = .8 ft per hr
Red candle burn rate 10/8 = 1.25 ft per hr
:
Let t = time when blue candle height will be 3 times height of red candle
:
Blue candle ht = 3*red candle height
(8 - .8t) = 3(10 - 1.25t)
8 - .8t = 30 - 3.75t
-.8t + 3.75t = 30 - 8
+2.95t = 22
t = 22/2.95
t = 7.457627 hrs
:
Find the minutes: .457627*60 = 27.4576 min
:
t = 7 hr 27 minutes
:
Check solution by finding the height of each candle after 7 hr 27 min (7.46 hrs)
8 - .8(7.46) = (blue candle)
8 - = 5.968 ft = 2.03 ft
:
10 - 1.25(7.46) = (red candle)
10 - 9.325 = .675 * 3 = 2.025 ~ 2.03, (Red candle 1/3 of Blue)
:
:
2. A bicycle wheel has a 12-inch radius. If you peddle at a rate of 60 revolutions per minute, how long will it take you to go 9 miles?
:
Find the circumference:
C = pi(2*12)
C = 75.4 inches
:
In 1 min at 60 rpm
60 * 75.4 = 4523.9 inches
Which is:
4523.9/12 = 377 feet per minute
:
9(5280)/377 = 126 minutes
:
:
3. A luxury cruise ship leaves New York on its way to London. When it is 180 miles from shore a helicopter is sent out to catch up with the ship. The helicopter's speed is ten times that of the ship. How far from New York does the helicopter catch up with the ship?
:
Let d = distance from New York when helicopter catches up
:
s = speed of ship
10s = speed of helicopter
:
Travel time will be the same for both: Time = dist/speed
:
Helicopter time = ship time
=
:
Multiply equation by 10s and you have:
D = 10(D-180)
D = 10D - 1800
D - 10D = -1800
-9D = -1800
D = -1800/-9
D = 200 miles
:
That makes sense; the helicopter travels 200 mi while the ship travels 20 mi
:
:
4. Meghan travels from A to B at 2 minutes per mile and returns over the same route at 2 miles per minute. Find her average speed, in miles per hour, for the whole trip.
:
Let D = distance one way
:
Speed in mph at 2 min/mile: 60/2 = 30 mph
:
Find the time to make the journey out: Time = Dist/speed
Time out = D/30
:
:
Speed in mph at 2 mi per min: 60 * 2 = 120 mph
:
Find the time to make the journey back: Time = Dist/speed
Time back = D/120
:
:
Total time = + = + = = ; (total time for round trip)
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Total distance for round trip = 2D
:
Average speed = Dist/time
:
Average speed = = 2D * = 2 * 24 = 48 mph
:
:
That seemed too low so chose a distance of 60 mi one way and see what happens:
Time out = 60/30 = 2 hr
Time back = 60/120 = .5 hrs
Total for the round trip = 2.5 hrs
:
Find av speed using that: 120/2.5 = 48 mph so I guess it's right
:
These were pretty tricky, let me know if I got any of them wrong.