Question

The speed of 3 ships are in the ration A:B:C. If they sail for the same distance, what is the ratio of the taken time.

Answer 1

Let the speeds be \(kA, ~kB,~ kC\), and the distance be \(x\).\[t_1 = \dfrac{x}{kA}\]\[t_2 = \dfrac{x}{kB}\]\[t_3 = \dfrac{x}{kC}\]\[\Rightarrow t_1 : t_2: t_3 = ~?\]

Answer 2

1/a:1/b:1/c

Answer 3

If I call with d the same distance, then, I can write:
\[d:d:d=At _{a}:Bt _{b}:Ct _{c}\]
so:
\[At _{a}:Bt _{b}:Ct _{c}=1:1:1\]
from the first two ratios, I can write:
\[At _{a}:Bt _{b}=1:1\]
and now, I apply the fundamental property of proportions, so:
\[\frac{ t _{b} }{ t _{a} }=\frac{ 1/B }{ 1/A }\]
similarly I get, if I consider the proportion between the second and third ratios

Answer 4

namely, i f I consider the proportion between the second and third ratios, I get:
\[\frac{ t _{b} }{ t _{c} }=\frac{ 1/B }{ 1/C }\]

Answer 5

@ParthKohli so is my answer corect

Answer 6

@ParthKohli

Answer 7

@Michele_Laino whats the answer cos I cant read ur latex

Answer 8

@perl a little help please

Answer 9

If I call with d the same distance, then, I can write:
d:d:d=At_a:Bt_b:Ct_c
so:
At_a:Bt_b:Ct_c=1:1:1
from the first two ratios, I can write:
At_a:Bt_b=1:1
and now, I apply the fundamental property of proportions, so:
t_b/t_a=(1/B)/(1/A)
similarly I get, if I consider the proportion between the second and third ratios
namely, i f I consider the proportion between the second and third ratios, I get:
t_b/t_c=(1/B)/(1/C)

Answer 10

so is the ratio of th time 1/a:1/b:1/c

Answer 11

@Michele_Laino ?

Answer 12

yes!

Answer 13

finally.. thanks

Answer 14

thanks!