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=(40)/(15) = (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.