Journey Paddling
Maths problems eigth grade?
Show all working:
1. Pump A can fill a tank in 5 minutes. Pump B can fill the same tank in 10 minutes. How long would it take to fill the tank when the two pumps work together?
2. In making one revolution, a car wheel travels 200cm. How fast are the wheels spinning, in revolutions per minute, when the car is travelling at 60km/h? (Answer to the nearest revolution per minute)
3. A girl paddles her kayak upstream from her home to her friends home, taking 2.5hours for the journey. She returns that afternoon in 1.5 hours. If the river is flowing at 2.5km/h, find:
(i) her paddling speed in still water
(ii) the distance to her friend's place
1. Given, A fills the tank (say) x ltr in 5 min
B fill x ltr in 10 min
Rate of filling tank of A is x/5 ltr/min
Rate of filling tank of B is x/10 ltr/min
Combined rate of filling the tank,
=x/5 + x/10
=3x/10 ltr/min
3x/10 ltr is filled in one minute
so x ltr is filled in 10/3 minute...(Unitary method)
Time it will take by both to fill the tank (x ltr) is 3.33 mins.
2. For this question let's convert all the units to some convinient unit say metre.
Distance travelled by wheel in one revolution 200cm=2m
Speed of car = 60km/hr
=60000m/hr
=60000/3600 m/min
=50/3 m/min
Now number of revolution per minute = 50/(3X2)
=25/3 rev/minute
=8.333 rev/minute
3. Let the girls paddling speed be x km/h
During upstream journey,
speed is (x-2.5) km/h
The distance travelled is (x-2.5)X2.5
During downstream journey the speed is,
(x+2.5) km/hr
The distance travelled is (x+2.5)X1.5
Therefore
(x-2.5)X2.5=(x+2.5)X1.5
2.5x - 6.25 = 1.5x +3.75
x=10 km/h
(i) her paddling spped in still water is 10 km/h
(ii) the distance to her friend's place is, (x - 2.5)X2.5
=(10-2.5)X2.5
=7.5X2.5
18.75 km
There you go!
www.up4adventures.co.uk estuary journey kayaking
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