Question

Place A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other they meet in 1 hour. What are the speeds of the two cars?

Answer 1

Hint:
First we will assume the speed of the car at place A and at place B to be any variable and then we will form equations using the information given in the question. From there, we will get two equations including two variables. We will solve these equations to get the value of the variables assumed.

Complete step by step solution:
Let the speed of car at place A be \[x~km/h\] and let the speed of car at place B be \[y~km/h\]
Thus, the relative speed of the cars when they travel in same directions is equal to $\left( x-y \right)km/h$
We know the distance between the place A and B is equal to 100 km.
It is given that they both meet in 5 hours when they travel in the same direction.
Therefore,
$t=5hours$
We know the formula;
$\text{distance}=\text{speed}\times \text{time}$
Substituting the value of distance, time and speed, we get
$\Rightarrow 100=\left( x-y \right)\times 5$
Dividing both sides by 5, we get
$\Rightarrow x-y=20$ ……….. $\left( 1 \right)$
The relative speed of the cars when they travel in same directions is equal to $\left( x+y \right)km/h$
We know the distance between the place A and B is equal to 100 km.
It is given that they both meet in 1 hours when they travel in the same direction.
Therefore,
$t=1hour$
We know the formula;
$\text{distance}=\text{speed}\times \text{time}$
Substituting the value of distance, time and speed, we get
$\Rightarrow 100=\left( x+y \right)\times 1$
On multiplying the terms, we get
$\Rightarrow x+y=100$ ……….. $\left( 2 \right)$
Adding equation 1 and equation 2, we get
$
   \underline{
   x+y=100 \\
  x-y=20 \\
} \\
  2x=120 \\
$
Dividing both sides by 2, we get
$\Rightarrow x=60$
Now, we will substitute the value of $x$ in equation 2.
$\Rightarrow 60+y=100$
Subtracting 60 from sides, we get
$
   \Rightarrow 60+y-60=100-60 \\
  \Rightarrow y=40 \\
$

Thus, the speed of car at place A is equal to $60km/h$ and the speed of car at place B is equal to $40km/h$.

Note:
Here we have used the formula; $\text{distance}= \text{speed} \times \text{time}$, here it means that the distance travel by any object is equal to the product of the speed of that object and the time taken by that object to travel that distance.