Anonymous
Anonymous asked in Education & ReferenceHomework Help · 3 weeks ago

# help me with math homework please ?

a boat can go 12 km along the water current in 2 hours. the return trip takes 3 hours against the water current. what is the speed of the boat in still water and the speed of the water current?

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• Downstream: 12km in 2 hours = 12/2 =  6kph

Upstream: 12 km in 3 hours = 12/3 = 4 kph

Average speed = (6 + 4)/2 = 5 kph

The speed of the boat in still water is 5 kph

6 - 5 = 1

or

5 - 4 = 1

The current is 1 kph

ANS Boat = 5 kph. Current is 1 kph

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• Let the boat's speed in still water = b and the river's speed = r

(b+r)*2 = 12km

2b+2r= 12km

(b-r)*3 = 12km

3b-3r = 12km Multiply equation by 2/3

2b-2r = 8  Subtract from 2b+2r = 12

4r = 4 so r = 1km/hr = current speed.

Substitute into 2b+2r=12

2b+2 = 12

2b = 10, b = 5km/hr = boat's speed in still water

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• let r= speed in still water km/hr

let c = rate of current km/hr

(r +c)2  = 12

(r-c) 3  =12

2r +2c  =12

3r-3c =12

multiply 1st by 3 and 2nd by 2

6r + 6c  = 36

6r - 6c   = 24

12r  = 60

r  = 60/12 =5 km/hr

speed in still water= 5 km/hr

2*5 + 2c = 12

10 + 2c =12

2c  = 12 -10

2c =2

c = 2/2 =1 km/hr

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