Question

First year students of Harvard university embarked on an excursion to Paris and travelled half the distance at 45km per hour and the other half at 55km per hour. Find the average speed for the whole journey

Answer 1

Step 1:

In this question, we are given the following:

First year students of Harvard university embarked on an excursion to Paris and travelled half the distance at 45km per hour and the other half at 55km per hour. Find the average speed for the whole journey.

Step 2:

The details of the solution are as follows:

`\begin{gathered} We\text{ can see that the total distance = 45 km + 55 km = 100 km} \\ Average\text{ distance = }\frac{45\text{ km + 55km}}{2}=\frac{100\text{ km }}{2}=\text{ 50 km} \end{gathered}`
`\begin{gathered} Time\text{ spent in the first half of the journey = }\frac{Average\text{ Distance}}{speed_1} \\ =\text{ }(50)/(45)\text{ hours} \end{gathered}`
`Time\text{ spent in the second part of the journey = }\frac{Average\text{ Distance}}{speed_2}`
`=\frac{50\text{ }}{55}\text{ hour}`

Then, the average speed for the whole journey will be:

`\frac{Total\text{ Distance}}{Time\text{ spent in the first journey + Time spent in the second journey}}`

`=\frac{100\text{ }}{((50)/(45))\text{ + \lparen}(50)/(55))}`
`=\text{ }(100)/((200)/(99))\text{ = 100 x }(99)/(200)=\text{ }(99)/(2)=\text{ 49.5 km per hour}`

CONCLUSION:

The average speed for the whole journey =

`49.\text{ 5 km per hour}`