Question

In a journey of 15 miles, two third distance was travelled with 40 mph and remaining with 60 mph. How much time does the journey take?

Answer 1

The first step in solving this question is to split the journey into 2 parts. In the first part of the journey,
`(2)/(3) * 15 = 10` miles are covered at a speed of 40 mph. In the second part the journey 5 miles are covered at a speed of 60 mph.

The equation to compute the time of a journey given the speed and distance is
`t=(d)/(s)` where
`t` is the time,
`s` is the speed and
`d` is the distance.

The time for the first part of the journey is calculated as shown below,

`t=(d)/(t) \\t=(10m)/(40mph) =(10)/(40) h`.

The time for the second part of the journey is calculated as follows,

`t=(d)/(t) \\t=(5m)/(60mph) =(5)/(60) h`.

The total time is the sum of the times taken to cover each part of the journey and is calculated as shown below,

`t=(10)/(40) h+(5)/(60) =(30+10)/(120) h=(40)/(120)h =(1)/(3) h`

The time to cover the journey is a third of an hour or 20 minutes.