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Question

The distance between the 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 per hour. If the distance between the cars after 2 hours is 34 km, find the speed of the cars.


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Solution

Step 1. Obtain the required equation.

The total distance between the two towns is 300km

The speed of one car is more than the other by 7kmperhour.

The distance between the cars after 2hours is 34km.

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

The speed of car-A is xkmhr

The speed of car-B is (x+7)kmhr

Use formula:

Distance=Speed×Time

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

Distance traveled by car-A in 2 hours is 2xkm

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

Distancebetweenthetwocarsafter2hours=Totaldistance-Distancetraveledbycar-A-Distancetraveledbycar-B:34=300-2x-(2x+14)

Step 2. Solve the equation to determine the required speed.

34=300-2x-(2x+14)⇒34=300-2x-2x-14⇒4x=300-34-14⇒4x=252⇒x=2524⇒x=63

The speed of car-A =x=63kmhr.

The speed of car-B (x+7)=63+7=70kmhr.
Hence, the speed of the cars are 63kmhr and 70kmhr.


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