How to show $\frac{300}{v} - \frac{300}{v+20} = 1.25$

Question

A man travels a distance of $300$ km. On his return journey his average speed increased by $20$ km/h and his journey time decreased by $1\frac{1}{4}$ hours. If $v$ is the average speed of his outward journey how can we show that: $$\frac{300}{v} - \frac{300}{v+20} = 1.25$$ I'm very stuck.

Answer 1

By the information you have, using $\text{speed}\cdot \text{time} = \text{distance}$ you can create two equations: $$\text{I:}\quad v\cdot t = 300\\ \text{II:}\quad (v+20)\cdot (t-1.25) = 300$$

Edit: Express $t$ from each equation, you get $$\text{I:}\quad t = \frac{300}{v}\\ \text{II:}\quad t = \frac{300}{v+20} + 1.25$$

Now compare substitute $t$ from the first equation into the second one. $$\frac{300}{v} = \frac{300}{v+20} + 1.25$$ Now you only have to subtract $\frac{300}{v+20}$.