Question

A car can reach a certain place in 12 hours at the speed of \[{\text{60 km/hr}}\]. By how much should the speed be increased so that it completes the journey in 10 hours ?

Answer 1

Hint:We are given with a car and two durations in which it is travelling. But we know that if the duration or we can say time of travelling is decreased it means the speed of the car is definitely increased. Thus, we will first find the distance it travels and then the speed that it needs to complete the same journey in 10 hours. After that we will find the difference in speed and that is nothing but the speed to be increased!

Formula used:
\[{\text{speed = }}\dfrac{{{\text{distance}}}}{{{\text{time}}}}\]
\[{\text{distance = speed} \times \text{time}}\]

Complete step by step answer:
In the first scenario the car travels with a speed of \[{\text{60 km/hr}}\] for 12 hours. So the total distance it covers is,
\[{\text{distance = speed}} \times{\text{ time}}\]
\[{\text{distance = 60}} \times {{12}}\]
On multiplying we get,
\[{\text{distance = 720 km}}\]

Now in the second scenario the speed is definitely increased because the same distance is covered in just 10 hours that is 2 hours earlier. So we can find the speed with the formula,
\[{\text{speed = }}\dfrac{{{\text{distance}}}}{{{\text{time}}}}\]
\[\Rightarrow {\text{speed = }}\dfrac{{{\text{720}}}}{{{\text{10}}}}\]
On dividing we get,
\[{\text{speed = 72 km/hr}}\]

That is the increased speed. But this is not the answer. We have to find the increased speed as compared to the original speed. Thus it is given by,
\[{\text{increased speed = 72 - 60}}\]
On subtracting we get,
\[\therefore {\text{increased speed = 12 km/hr}}\]

Hence the increased speed so that the car completes the journey in 10 hours is 12 km/hr.

Note:If speed is increased the time required to travel the same distance definitely decreases! This is the only relationship used here. Also note that the units are all in the same system that is MKS. But if they are in different systems in case, then first the systems should be equalized and then proceed to the solution.