Algebraic Speed Distance And Time Question GCSE

Question

Question:

What I did:

$x$ = miles $\frac{x}{60mph}$ and $\frac{x}{45mph}$

and so $x = 60t$ and $x = 45t$

I don't know what to do from here to work out time.

Thankyou, any help is appreciated!

Answer 1

You should say $\frac x{60mph}$ is the outward time and $\frac x{45mph}$ is the return time. Just writing the two fractions down leaves it unclear what they mean and lead to your assumption that the two times are the same.

Then it is clear that the total time is $7hours=\frac x{60mph}+\frac x{45mph}$ Now multiply by something to clear the fractions, like $180$ because it is the least common multiple of $45$ and $60$, giving $$7\cdot 180=3x+4x\\180=x$$