Distance between two places A and B is 210 km. Two cars travel simultaneously from A and B in opposite directions and the distance between them after 3 hours is 54km. If the speed of one car is less than that of other by 8 km/h, find the speed of each car.

Given: 

Distance between two places A and B $= 210\ km$.

Speed of one car is less than the other by $8\ km/hr$.

Distance between the cars after 3 hours is $54\ km$.

To find: 

We have to find the speed of the cars.

Solution:

Let the car that starts from place A be P and the car that starts from place B be Q.

Let speed of car P $=x$ km/hr

So, speed of car Q $=(x\ -\ 8)$ km/hr  

We know that,

Distance = Speed $\times$ Time

Now, distance between the cars after 3 hours is 54 km;

Distance travelled by car-P in 3 hours = $3x$ km  

Distance travelled by car-Q in 3 hours = $3(x\ -\ 8)$ = $(3x\ -\ 24)$ km

Distance between the two cars after 3 hours = Total distance $-$ (Distance travelled by car-P $+$ Distance travelled by car-Q)

$54\ =\ 210\ -\ 3x\ -\ (3x\ -\ 24)$

$54\ =\ 210\ -\ 6x\ +\ 24$

$54\ =\ 234\ -\ 6x$

$6x\ =\ 234\ -\ 54$

$6x\ =\ 180$

$x\ =\ \frac{180}{6}$

$x\ =\ 30$

Therefore,

Speed of car-P = $x$ = 30 km/hr

Speed of car-Q = $(x\ -\ 8)$ = $30\ -\ 8$ = 22 km/hr  

So, speeds of the cars are 30 km/hr and 22 km/hr. 

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Updated on: 10-Oct-2022

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