Question

The time needed to travel from one place to another is inversely proportional to the speed. A person travelling 72km/hr can go from Dehradun to Lucknow in 10 hours. How fast must he travel to make up the trip in 9 hours?

Answer 1

Hint: We are given with a standard condition that time needed to travel from one place to another is inversely proportional to the speed. That is if speed is increased, time required is decreased and vice versa. Now what we will do is use the standard formula of time, distance and speed. We will calculate the total distance travelled and then we will divide that distance by the number of hours to get the speed and compare that speed with the previous and find by how much the speed should be increased.

Complete step by step solution:
Given that, A person travelling 72km/hr can go from Dehradun to Lucknow in 10 hours
Now as we know,
\[{{distance = speed \times time}}\]
So on submitting the values,
\[{{distance = 72 \times 10 = 720km}}\]
Now this same distance is to be travelled in 9 hours that is in less time. So definitely the speed should be increased.
So we will rearrange the formula now,
\[{{speed = }}\dfrac{{{{distance}}}}{{{{time}}}}\]
So on submitting the values,
\[{{speed = }}\dfrac{{{{720}}}}{9} = 80\] km/hr
Thus the speed should now be 80 km/hr.
So the person should travel with a speed of 80 km/hr to cover the same distance in 9 hours.
So, the correct answer is “ 80 km/hr”.

Note: Note that, only one formula is sufficient to answer this question. That relates time, distance and speed. We know that these are interconvertible according to our needs. Also always focus on the units in these types of problems ; all units should be in the same system either CGS or MKS. And if they are not then make them the same first.