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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.