Question

An airplane covered a distance of 400 km at an average speed of x km/h. On the return journey, the speed was increased by 40 km/h. Write down an expression for the time taken for (i) the onward journey (ii) the return journey.

Answer 1

Hint: The formula for the speed of an object is \[v = \dfrac{d}{t}\]. Use this to find the expression for the time in terms of distance and speed and substitute the given values to find the answer.

Complete step-by-step answer:
The speed of an object is defined as the distance covered by the object in unit time. It is the ratio of total distance covered to the total time taken.

The speed, ‘v’, of an object covering a distance ‘d’ in time ‘t’, is given as follows:

\[v = \dfrac{d}{t}..........(1)\]

The expression for the time taken in terms of speed and distance is given from equation (1)

as follows:

\[t = \dfrac{d}{v}..........(1)\]

In this problem, it is given that the airplane covers a distance of 400 km at an average speed

of x km/h.

Then the time taken for the onward journey is 400 km divided by x km/h.

\[{t_{onward}} = \dfrac{{400}}{x}hr\]

The speed of the airplane is increased by 40 km/h when it returns, while it covers the same

distance as the onward journey.

Then the time taken for the return journey is 400 km divided by (x + 40) km/h.

\[{t_{return}} = \dfrac{{400}}{{x + 40}}hr\]

Note: Do not forget to write the unit for the time in terms of hours when you write the answer. The total time can be determined from average speed, instantaneous speed is not required.