1. Frank and Ernest start jogging on a 110m circular track. They begin at the same time and from the same point but jog in opposite directions, one at per second and the other at per second. How many times will they meet during the first 15 minutes of jogging?
2. Two candles of the same height are lit at the same time.. The first is consumed in four hours, the second in three hours. Assuming that each candle burns at a constant rate, how many hours after being lit was the first candle twice the height of the second?
3. If a:b = 3:4 and a: (b+c)= 2:5, find the value of a:c.
4.
5. The volume of two boxes are in the ratio 3:8. If the volume of the larger box is more than the volume of the smaller box, find the volume of each box.
Express each of the following with denominator 1:
6.
7.
Simplify / Evaluate
8.
Simplify
9.
Solve
10.
Thank you guys.
Hi,
to #1.: The distance between the two joggers increases by 5 m/s. Together they need 22 s to run the full distance of 110 m.
15 min = 900 s. Therefore they meet
#3.: From the first equation you get: . Plug in this term into the 2nd equation:
. After a few steps of simplification you get:
to #4.: Split this "chain of equalities" into 3 equations and solv for a, b and c:
(Remark: There doesn't exist an unique solution! I've got
to #5.:
Let V be the volume of the smaller box. Then you have:
Solve for V. You should get V = 225 cm³
to #10:
Are you sure that you can't solve this equation? (Divide both sides by 9 [you do this to get 1 as the coefficient of x because you want to know the value of one x]. For confirmation only: I've got x = 3)[/QUOTE]
Ah dammit, stupid Latex. It was 9^x. So x is an exponent.
Hello, Rocher!
The first candle is consumed in 4 hours.2. Two candles of the same height are lit at the same time.
The first is consumed in four hours, the second in three hours.
Assuming that each candle burns at a constant rate, how many hours
after being lit was the first candle twice the height of the second?
. . In one hour, iof the candle is gone.
. . In hours, of the candle is gone.
In hours, there will be: of the candle left.
The second candle is consumed in 3 hours.
. . In one hour, of the candle is gone.
. . In hours, of the candle is gone.
In hours, there will be of the candle left.
If the first candle is twice the height of the second candle,
. . we have: .
Now solve for
We have: . .[1]3. If and ,
find the value of
And: . .[2]
Substitute [1] into [2]: .
Therefore: .
We have: .8. Simplify: .
Since the problem is way too simple, I'll assume that it says: .10. Solve: . . ??
We have: .
Therefore: .