Question

The speed of three cars are in the ratio of 5 : 4 :6. the ratio between the time taken by them to travel the same distance is:

Answer 1

Answer:

The ratio of the time taken by the cars will be 12: 15: 10

Solution:

Given, the ratio of the three car’s speed will be 5 : 4 : 6

We know,  

$\text { Speed } = \frac { \text {distance} } { \text {time} }$

Since, the distance is same for the given cars,  

Taking distance = D,

$\text { Speed } = \frac { \text {D} } { \text {time} }$

Let the time taken by the 3 cars be termed as $t_1, t_2, t_3.$

Given,  

Ratio of Speeds = 5:4:6

$Speed_1:Speed_2:Speed_3=5:4:6$

$\begin{aligned} \left( \frac { D } { t _ { 1 } } \right) : \left( \frac { D } { t _ { 2 } } \right) : \left( \frac { D } { t _ { 3 } } \right) & = 5 : 4 : 6 \\\\ \left( \frac { 1 } { t _ { 1 } } \right) : \left( \frac { 1 } { t _ { 2 } } \right) : \left( \frac { 1 } { t _ { 3 } } \right) & = 5 : 4 : 6 \end{aligned}$

$t _ { 1 } : t _ { 2 } : t _ { 3 } = \frac { 1 } { 5 } : \frac { 1 } { 4 } : \frac { 1 } { 6 }$

LCM of 5, 4 and 6 will be 60.

$\begin{array} { l } { t _ { 1 } : t _ { 2 } : t _ { 3 } = \frac { 12 } { 60 } : \frac { 15 } { 60 } : \frac { 10 } { 60 } } \\\\ { t _ { 1 } : t _ { 2 } : t _ { 3 } = 12 : 15 : 10 } \end{array}$

Hence, the ratio of the time taken by the cars will be 12: 15: 10

Answer 2

Answer:

$\\Ratio \: of \: time\: taken\\ \: by \: three \: cars\\=12:15:10$

Step-by-step explanation:

Given speed of three cars are in the ratio 5:4:6

Let Speed of first car = 5x

Speed of second car = 4x

Speed of third car = 6x

Distance travelled = d

$We\: know \: that \\</p><p>\boxed {Time = \frac{distance}{speed}}$

$Now , \\Ratio \: of \: time\: taken\\ \: by \: three \: cars\\ =\frac{d}{5x}:\frac{d}{4x}:\frac{d}{6x}\\=\frac{1}{5}:\frac{1}{4}:\frac{1}{6}$

/* LCM(5,4,6)=60*/

$=\frac{60}{5}:\frac{60}{4}:\frac{60}{6}\\=12:15:10$

Therefore,

$\\Ratio \: of \: time\: taken\\ \: by \: three \: cars\\=12:15:10$

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