Question

At 8am,Ming Wei started travelling from Town A to Town B.At 8:40am, Ali started travelling from Town B to Town A.Mingwei's speed and Ali's speed were 45km/h and 35km/h respectively.They did not change their speeds throughout the journey.When they met each other,their distance from Town A was twice their distance from Town B.Find the distance between Town A and Town B.

Answer 1

Let's write some equations.

Mingwei's distance from Town A after $x$ hours from 8:00 is $45x$.

Ali's distance from Town B after $x$ hours is $30x-20$, since he doesn't start walking for 40 minutes.

When Mingwei's distance is twice Ali's, they've met up (since their distance from Town A is twice their distance from Town B).

So, this gives $45x=60x-40$, so $15x=40$, so $x=\frac{40}{15} = \frac{8}{3}$, so the time is 10:40.

After $\frac83$ hours, Mingwei has traveled $45 * 8 / 3 = 120$ kilometers while Ali has traveled sixty, so the distance between the towns is $180$ kilometers.