Question

An airline Concorde flies ${\rm{2000}}\,{\rm{km}}$ at a speed of ${\rm{1600}}\,{\rm{km/h}}$ and then returns due to bad weather at a speed of ${\rm{1000}}\,{\rm{km/h}}$. Find the average speed for the whole trip.

Answer 1

Hint: In this solution, first, we have to find both the travel time of the up and down trip of the flight using the given distance dividing with the speed. For that we need to use the formula ${\rm{Time}} = \dfrac{{{\rm{distance}}}}{{{\rm{speed}}}}$. Once we get their time, we can calculate the total time. After calculating the total distance, we can find the average speed of the flight by dividing the total distance with total time.

Complete answer:
Here,
First we compute for the time in speed $1$,
Step I,
We know that,
${\rm{Time}}\left( {\rm{1}} \right){\rm{ = }}\dfrac{{{\rm{distance}}}}{{{\rm{speed}}}}$
$ = \dfrac{{{\rm{2000}}\,{\rm{km}}}}{{{\rm{1600}}\,{\rm{km/hr}}}}$
$ = {\rm{1}}{\rm{.25}}\,{\rm{hrs}}$
Again,
Since, the airline just returned.
Therefore,
We compute for the time in speed $2$,
We know that,
${\rm{Time}}\left( 2 \right){\rm{ = }}\dfrac{{{\rm{distance}}}}{{{\rm{speed}}}}$
$ = \dfrac{{{\rm{2000}}\,{\rm{km}}}}{{{\rm{1000}}\,{\rm{km/hr}}}}$
$ = {\rm{2}}\,{\rm{hrs}}$
Step II,
Now, we solve for the total time and distance.
Therefore,
Total $ = $Time $\left( 1 \right)$$ + $Time$\left( 2 \right)$
$ = \left( {{\rm{1}}{\rm{.25 + 2}}} \right)\,{\rm{hrs}}$
$ = 3.25\,{\rm{hrs}}$ ……(1)
Now,
Since it is a round trip, we will add the total distance.
Therefore,
Distance$ = $${\rm{2}}\left( {{\rm{2000}}\,{\rm{km}}} \right)\,$
$ = {\rm{2}} \times {\rm{2000}}\,{\rm{km}}$
$ = 4{\rm{000}}\,{\rm{km}}$ ……(2)

We need to find the average speed, by using the equations (1) and (2)
Average Speed$ = \dfrac{{{\rm{Total Distance}}}}{{{\rm{Total Time}}}}$
$ = \dfrac{{{\rm{4000}}\,{\rm{km}}}}{{{\rm{3}}{\rm{.25}}\,{\rm{km/hr}}}}$
$ = {\rm{1230}}{\rm{.77 km/hr}}$

Hence, the average speed for the whole trip is ${\rm{1230}}{\rm{.77 km/hr}}$.

Note: Speed of an object means the distance covered at a particular time. Here we have to determine the speed of the flight for the given data. In step I we have to determine the average time using the distance and time by using the formula time equals distance divided by speed in the first trip of the flight. Again, we have to determine the average time using the distance and time by using the formula time equal distance divided by speed in the second trip of the flight which is a round trip. Then, in step II we add the total time on both the trips of the flight. Also, we need to find the total distance of the flight (up and down trip of the flight). Then, we find the average speed by dividing the total distance by total time.