Question 202048: 1)A small plane took 3 hours to fly 960 km from Ottawa to Halifax with a tail wind. On the return trip, flying into the wind, the plane took 4 hours. Find the wind speed and the speed of the plane in still air.
2)Maria drove from Owen Sound to Ottawa, a distance of 550km. The trip took 7h. Maria drove at 70km/h for part of the trip and at 85km/h for the remainder of the trip. How far did she drive at 70km/h?
3)The Mackenzie, the longest river in Canada, is 1056 km longer than the Yukon, the second longest river. The total length of the two rivers is 7426km. Find the length of each river.
4) Zach invested in a term deposit that paid 4% interest per year and in a municipal bond that paid 6% interest per year. If he invested a total of $13000 and earned $700 interest in a year, how much did he invest at each rate?
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! 1)A small plane took 3 hours to fly 960 km from Ottawa to Halifax with a tail wind. On the return trip, flying into the wind, the plane took 4 hours. Find the wind speed and the speed of the plane in still air.
Use d = rt
960 = r*3 going
960 = r*4 returning
960 = (A + w)*3 (airspeed + windspeed)
960 = (A - w)*4 (airspeed - windspeed)
3A + 3w = 960 --> A + w = 320
4A - 4w = 960 --> A - w = 240
Add the 2 eqns
2A = 560
A = 280
--------
w = 40
--------
Airplanes don't use kilometers per hour, they use knots. Boats also use knots.
--------------------
2)Maria drove from Owen Sound to Ottawa, a distance of 550km. The trip took 7h. Maria drove at 70km/h for part of the trip and at 85km/h for the remainder of the trip. How far did she drive at 70km/h?
t = time driving at 70
70t + 85(7-t) = 550
70t + 595-85t = 550
-15t = -45
t = 3 hours at 70 kph
---------------------
3)The Mackenzie, the longest river in Canada, is 1056 km longer than the Yukon, the second longest river. The total length of the two rivers is 7426km. Find the length of each river.
M + Y = 7426
M = Y + 1056
Sub for M in 1st eqn
Y+1056 + Y = 7426
2Y = 6370
Y = 3185 km
M = 4241 km
------------
4) Zach invested in a term deposit that paid 4% interest per year and in a municipal bond that paid 6% interest per year. If he invested a total of $13000 and earned $700 interest in a year, how much did he invest at each rate?
A = Amount at 4%
A*0.04 + (13000 - A)*0.06 = 700
4A + 78000 - 6A = 70000
-2A = -8000
A = $4000 at 4%
-----------------
$9000 at 6%
|
|
|
