Two candles of the same height are lighted at the same time. The first is consumed in 4hrs and second is consumed in 3h. assuming that each candle burns at a constant rate,in how many hrs after being lighted was the first candle twice the height of the second
Answers
Answer:
6
Step-by-step explanation:
Given Two candles of the same height are lighted at the same time. The first is consumed in 4hrs and second is consumed in 3h. assuming that each candle burns at a constant rate,in how many hrs after being lighted was the first candle twice the height of the second.
So let the length of the first candle consumed in 1 hour be 4 mtrs
and let the length of the second candle consumed in 1 hour be 3 mtrs
Now let us assume both the candle was consumed in x hours.
So 4 x 3 = 12
So now since it is twice we can write the equation as
12 - 4 x = 2(12 - 3 x)
12 - 4 x = 24 - 6 x
2 x = 12
x = 6 hours
Step-by-step explanation:
Let h be the height of the candle
speed of First Candle =
4
h
speed of Second Candle =
3
h
how many hours after being lit was the first candle twice the height of the second?
let r be the height of the second candle at that time (t).
r=h−(
3
h
)t
at the same time(t), the height of the first candle must be 2r
2r=h−(
4
h
)t
2(h−(
3
h
)t)=h−(
4
h
)t
2h−(
3
2
)ht=h−(
4
1
)h
2−(
3
2
)t=1−(
4
1
)t
t(
3
2
−
4
1
)=1
t=
5
12
hr or 2.4hr.