Question

A car travels 120 km from A to B at 30 km per hour but returns the same distance at 40 km per hour. The average speed for the round trip is closest to:
(a) 33 km/hr
(b) 34 km/hr
(c) 35 km/hr
(d) 36 km/hr
(e) 37 km/hr

Answer 1

Hint: First find the time taken by the car when it was travelling with a speed of 30 km per hour and 40 km per hour by using the speed-distance –time relation \[t=\dfrac{d}{s}\]. Then find the total time taken and total distance travelled by the car in both the cases. By dividing the total distance with total time taken we get average speed.

Complete step-by-step answer:
We know the speed-distance-time relation is given as \[t=\dfrac{d}{s}\], where d is the distance travelled in km, s is the speed of the body in km/hr and t is the time taken in hours by the body to travel the signified distance (d).
Applying the above relation to find the time taken by the car when speed is = 30 km per hour,
By substituting d = 120 km in the above mentioned formula we get,
\[t=\dfrac{120}{30}\]
On dividing 120 by 30 the time taken in hours is,
t = 4
Applying the above relation to find the time taken by the car to return when speed s = 40 km per hour,
By substituting d = 120 km in the above mentioned formula we get,
\[t=\dfrac{120}{40}\]
On dividing 120 by 40 the time taken in hours is,
t = 3
We know the formula for the average speed of a body is given as \[S=\dfrac{D}{T}\], where S is the average speed of the body, D is the total distance travelled and T is the total time taken.
We know the total distance traveled D can be calculated as the sum of distances travelled in when the speed of the body was 30 km/hr and 40 km/hr.
The above said statement can be written mathematically as,
D = 120 + 120
On adding 120 and 120 we get total distance travelled D in km as,
D = 240
We know the total time taken T can be calculated as the sum of time taken when the speed of the body was 30 km/hr and 40 km/hr.
The above said statement can be written mathematically as,
T = 4 + 3
On adding 4 and 3 we get the total time taken T in hours as,
T = 7
Applying the formula for average speed S mentioned above we get,
By substituting the values of D = 240 km and T = 7 hours average speed S is,
\[S=\dfrac{240}{7}\]
On dividing 240 by 7 we get the average speed in km/hr as,
S = 34.28
By approximating the value we get average speed S = 34 km /hr.
Hence option (b) is the correct answer.

Note: Alternatively average speed can also be calculated as the ratio of average distance travelled to the average time taken. Average distance is the sum of all the distance values divided by the number of distances. Similarly the average time can also be calculated the same way. On dividing the average distance with average time taken we will get the average speed of the car.