The distance between two towns is 300 km. Two cars start simultaneously from these towns and move towards each other. The speed of one car is more than the other by 7 km/hr. If the distance between the cars after 2 hours is 34 km, find the speed of the cars.

Given: 

Distance between two towns = 300 km

Speed of one car is more than the other by 7 km/hr

Distance between the cars after 2 hours is 34 km

To find: Here we have to find the speed of the cars.

Solution:

Let the car start from town 1 be Car-A and car start from town 2 be Car-B.

Let speed of car-A = $x$ km/hr

So, speed of car-B = $(x\ +\ 7)$ km/hr  

We know that:

Distance = Speed $\times$ Time

Now, distance between the cars after 2 hours is 34 km;

Distance traveled by car-A in 2 hours = $2x$ km  

Distance traveled by car-B in 2 hours = $2(x\ +\ 7)$ = $(2x\ +\ 14)$ km

Distance between the two cars after 2 hour = Total distance $-$ Distance traveled by car-A $-$ Distance traveled by car-B

$34\ =\ 300\ -\ 2x\ -\ (2x\ +\ 14)$

$34\ =\ 300\ -\ 4x\ -\ 14$

$34\ =\ 286\ -\ 4x$

$4x\ =\ 286\ -\ 34$

$4x\ =\ 252$

$x\ =\ \frac{252}{4}$

$x\ =\ 63$

Therefore,

Speed of car-A = $x$ = 63 km/hr

Speed of car-B = $(x\ +\ 7)$ = $63\ +\ 7$ = 70 km/hr  

So, speed of the cars are 63 km/hr and 70 km/hr.

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Updated on: 10-Oct-2022

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