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.

Answer 1

Step 1. Obtain the required equation.

The total distance between the two towns is $300\mathrm{km}$

The speed of one car is more than the other by $7\mathrm{km}\mathrm{per}\mathrm{hour}.$

The distance between the cars after $2\mathrm{hours}$ is $34\mathrm{km}.$

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

The speed of car-A is $x\frac{\mathrm{km}}{\mathrm{hr}}$

The speed of car-B is $(\mathrm{x}+7)\frac{\mathrm{km}}{\mathrm{hr}}$

Use formula:

$\mathrm{Distance}=\mathrm{Speed}\times \mathrm{Time}$

Now, the distance between the cars after $2$ hours is $34\mathrm{km}.$.

Distance traveled by car-A in $2$ hours is $2x\mathrm{km}$

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

$\begin{array}{rcl}\mathrm{Distance}\mathrm{between}\mathrm{the}\mathrm{two}\mathrm{cars}\mathrm{after}2\mathrm{hours}& =& \mathrm{Total}\mathrm{distance}-\mathrm{Distance}\mathrm{traveled}\mathrm{by}\mathrm{car}-\mathrm{A}-\mathrm{Distance}\mathrm{traveled}\mathrm{by}\mathrm{car}-\mathrm{B}:\\ 34& =& 300-2\mathrm{x}-(2\mathrm{x}+14)\end{array}$

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

$$\begin{gathered} 34=300-2x-(2x+14) \\ \Rightarrow 34=300-2x-2x-14 \\ \Rightarrow 4x=300-34-14 \\ \Rightarrow 4x=252 \\ \Rightarrow x=\frac{252}{4} \\ \Rightarrow x=63 \end{gathered}$$

The speed of car-A $=\mathrm{x}=63\frac{\mathrm{km}}{\mathrm{hr}}$.

The speed of car-B $(\mathrm{x}+7)=63+7=70\frac{\mathrm{km}}{\mathrm{hr}}$.
Hence, the speed of the cars are $63\frac{\mathrm{km}}{\mathrm{hr}}$ and $70\frac{\mathrm{km}}{\mathrm{hr}}$.