Hello I've received holiday homework from my text book and i cant seem to work ou these questions. anyone know the working outs?i saw the answer from the back of the book but i don't just want to copy it i want to understand it
thanks.:]
1)Two tanks contain equal amounts of water. They are connected by a pipe and 3000 litres of water is pumped from one tank to the other. One tank then contains 6 times as much water as the toher. How many litres of water did each tank contain originally.
Answer:4200L
2)a boy is 24 years younger than his father. In 2 years time the sum of thier ages will be 40. find the present ages of father and son.
Answer: father-30 son-6
3)A man travels from A to B at 4km/h and from B to A at 6km/h. the total journey takes 45 minutes. find the distance traveled
answer- 3.6km
4) jess walked for 45 minutes at 3km/h and then ran for half an hour at xkm/h. At the end of that time she was 6km from the starting point. find the value of x.
The relevant equation here is
Let the distance from A to B (or B to A) be d.
From A to B we have
where t is the take it takes for the trip.
From B to A we have
where T is the time it takes for the trip.
And we also know that
(Use the unit hours for the time since the speed is given in km/h.)
This gives you the three equations
-Dan
[QUOTE=fresh_;162147]Hello I've received holiday homework from my text book and i cant seem to work ou these questions. anyone know the working outs?i saw the answer from the back of the book but i don't just want to copy it i want to understand it
thanks.:]
1)Two tanks contain equal amounts of water. They are connected by a pipe and 3000 litres of water is pumped from one tank to the other. One tank then contains 6 times as much water as the toher. How many litres of water did each tank contain originally.
Answer:4200L
Let us say each tank has x liters of water initially.
So after 3000L is transfered from one tank to the other,
one tank has now (x -3000) liters, and the other has (x +3000) liters.
Then the problem says the tank with more water has now 6 times as much water than the tank with less water, meaning,
(x +3000) = 6*(x -3000)
So, simplifying that,
x +3000 = 6x -18,000
x -6x = -18,000 -3000
-5x = -21,000
x = -21,000 /(-5)
x = 4200L -------same as the book answer.
- - - - - - - -
4) jess walked for 45 minutes at 3km/h and then ran for half an hour at xkm/h. At the end of that time she was 6km from the starting point. find the value of x.
distance = rate * time
d = rt
The units must be consistent. If x is in km/hr, then time must be in hours.
45minutes = 45/60 = 3/4 hr.
(3/4)(3) +(1/2)(x) = 6 ------this is what the problem says.
So,
9/4 +x/2 = 6
Clear the fractions, multiply both sides by 4,
9 +2x = 24
2x = 24 -9
x = 15/2 = 7.5 ----------answer.
THANKS GUYS FOR THE HELP!!, I REALLY NEEDED IT
theirs one more i got stuck on for this exercise
a shopkeeper buys a crate of eggs at $1.50 per dozen. He buys another crate, containing 3 dozen more than the first crate, at $2.00 per dozen. He sells them all for $2.50 a dozen and makes $15 profit. how many dozens were there in each of the crates.
ANSWER- 9 AND 12 DOZEN
THANKS AGAIN
let there be x dozen eggs that he bought for 1.5$
therfor his expenditure will be=1.5x $
now he bought 3 dozen more eggs than before i.e x+3 for 2$ per dozen, therfor his expenditure will be=2(x+3)$
so his total expenditure is
[1.5x +2(x+3)]$
now total dozen of eggs =x+x+3=2x+3 these were sold for 2.5$ per dozen therfor total selling price=2.5(2x+3) $
(profit=total selling price-expenditure) profit is given to be=15$ therefor
2.5(2x+3)-[1.5x +2(x+3)]=15
5x+7.5-1.5x-2x-6=15
1.5x=13.5
x=9
so intially there were 9 dozen eggs. Since second time shopkeeper took 3 dozen more eggs than previous time so second time there were 9+3=12 dozen eggs