# Places A and B are 80 km apart from each other.A car starts from A and other from B at the same time.If they move in the same direction,they meet in 8 hours and if they move in opposite direction they meet in 1 hour and 20 minutes.find speed ?

Aug 2, 2018

The speeds are ${v}_{A} = \frac{70}{2} = 35 k m {h}^{-} 1$ and ${v}_{B} = 25 k m {h}^{-} 1$

#### Explanation:

Let the speeds of the cars be

$= {v}_{A} k m {h}^{-} 1$

and

$= {v}_{B} k m {h}^{-} 1$

Firstly, for the cars moving in the same direction

Let the distance travelled by the second car be $= \mathrm{dk} m$

Then,

$80 + d = 8 {v}_{A}$

$d = 8 {v}_{B}$

Combining these $2$ equations

$80 + 8 {v}_{B} = 8 {v}_{A}$

$8 \left({v}_{A} - {v}_{B}\right) = 80$

$\left({v}_{A} - {v}_{B}\right) = 10$................................$\left(1\right)$

Secondly, for the cars moving in the opposite direction

Let the distance travelled by the second car be $= x k m$

Then,

$80 - x = \frac{4}{3} {v}_{A}$

$x = \frac{4}{3} {v}_{B}$

Combining these $2$ equations

$80 - \frac{4}{3} {v}_{B} = \frac{4}{3} {v}_{A}$

$\frac{4}{3} \left({v}_{A} + {v}_{B}\right) = 80$

${v}_{A} + {v}_{B} = 60$.........................................$\left(2\right)$

Solving equations $\left(1\right)$ and $\left(2\right)$

${v}_{A} = \frac{70}{2} = 35 k m {h}^{-} 1$

${v}_{B} = 25 k m {h}^{-} 1$