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, $\frac{2}{3} \times 15 = 10$ 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 $t=\frac{d}{s}$ 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,

$t=\frac{d}{t} \\t=\frac{10m}{40mph} =\frac{10}{40} h$.

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

$t=\frac{d}{t} \\t=\frac{5m}{60mph} =\frac{5}{60} h$.

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

$t=\frac{10}{40} h+\frac{5}{60} =\frac{30+10}{120} h=\frac{40}{120}h =\frac{1}{3} h$

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