Question

The distance between two places a and b on the road is seventy kilometers. A car starts from a and another from b. If they travel in the same direction, they will meet after seven hours. If they travel towards each other, they will meet after one hour. Find the speeds of both the cars.

Answer 1

Hint: Any two objects will meet only when the net distance travelled by them will be equal. In this case, if we assume the speeds of cars, as time is given, we can find out the distance travelled by car a and b easily and equate their distance travelled. We can then find out the speeds of the cars.

Formula used: $v=\dfrac{s}{t}$

Complete step by step answer:
Let us now assume the speeds of cars a and b as $v,{{v}_{1}}$respectively. Now, when the two cars a and b are travelling in the same direction, it is given that they meet after seven hours.
That means,
$\begin{align}
  & {{S}_{a}}={{S}_{b}}+70 \\
 & v(7)={{v}_{1}}(7)+70 \\
 & v={{v}_{1}}+10 \\
\end{align}$
Let’s keep this equation aside and find out the relation when two cars a and b move towards each other.
In this case, the net distance is equal to seventy.
$\begin{align}
  & 70={{S}_{a}}+{{S}_{b}} \\
 & 70=v+{{v}_{1}} \\
\end{align}$
Now, work out on both the above equations and find out the values of speeds of the cars a and b.
We get,
$v=40kmph,{{v}_{1}}=30kmph$

Therefore, the speeds of car a and car b are $40kmph,30kmph$ respectively.

Additional Information: Speed is defined as the rate at which an object or body covers certain distance over a period of time. When the speed is constant, time is directly proportional to distance. Also, when time is constant, speed is directly proportional to distance. Simply, speed is distance divided by the time taken. Units of speed in SI unit system is meter per second. In normal day life, we use the unit of speed as kilometers per hour. In countries like the UK or US, miles per hour is the unit to measure the speed of the bodies. In air and marine transport systems, units of speed are used.

Note: Speed is the distance divided by the time taken whereas velocity is the displacement divided by the time taken. Sped is a scalar quantity whereas distance is a vector quantity. When the direction of travel is important in the question, take care whether the speed of the object is given or the velocity.