Question

A car travels along four sides of a square at speeds of \[100,200,300\& 400\] km/hr. Find average speed
A. \[192km/hr\]
B. \[194km/hr\]
C. \[196km/hr\]
D. \[198km/hr\]

Answer 1

Hint: Here we have to find the average speed of the car so we will need the total distance travelled and the total time taken. So very first we will consider s as the length of the side of the square. So total distance travelled will be 4s. Again the total time will be calculated as the each side of the square divided by the speed with which it travels. Thus using the formula for average speed we will calculate the average speed of the car.

Complete step by step solution:
Let’s look at the figure below. The situation is somewhat like this.
Now we know that,
 \[{\text{speed}} = \dfrac{{{\text{distance}}}}{{{\text{time}}}}\]
So the total time required to travel is calculated as the sum of all times required to travel the four sides of the square.
Thus total time is given as,
 \[tota{l_{time}} = \dfrac{s}{{100}} + \dfrac{s}{{200}} + \dfrac{s}{{300}} + \dfrac{s}{{400}}\]
Taking LCM we get,
 \[tota{l_{time}} = \dfrac{{12s + 6s + 4s + 3s}}{{1200}}\]
On adding the terms we get,
 \[tota{l_{time}} = \dfrac{{25s}}{{1200}}\]
This is the total time required.
Now we know that total distance travelled is the perimeter of the square. Thus
 \[tota{l_{dis\tan ce}} = 4s\]
Now to calculate average speed we will use the formula,
 \[{\text{Averag}}{{\text{e}}_{{\text{speed}}}} = \dfrac{{{\text{tota}}{{\text{l}}_{{\text{distance}}}}}}{{{\text{tota}}{{\text{l}}_{{\text{time}}}}}}\]
Putting the results above obtained,
 \[{\text{Averag}}{{\text{e}}_{{\text{speed}}}} = \dfrac{{4s}}{{\dfrac{{25s}}{{1200}}}}\]
Cancelling s terms we get,
 \[{\text{Averag}}{{\text{e}}_{{\text{speed}}}} = \dfrac{{4 \times 1200}}{{25}}\]
On dividing by 25 we get,
 \[{\text{Averag}}{{\text{e}}_{{\text{speed}}}} = 4 \times 48\]
On multiplying we get,
 \[{\text{Averag}}{{\text{e}}_{{\text{speed}}}} = 192km/hr\]
This is our answer. Thus option A is the correct answer.
So, the correct answer is “Option A”.

Note: Here note that we have to find the average speed of the car. They have given the four different speeds for four same distances. This can create confusion. But we just have to remember the formula that speed is the ratio of distance and time. We have the clarity of distance but not of time. So we took help of given data to find the time constraint.