# Question 83f7e

Sep 13, 2016

They will meet at a point X 118 m from where A started after 17 s.

#### Explanation:

A stackrel(color(white)(xxxxxxxxxxxxxxxxxxxxxx))(color(red)(rarr) Xstackrel(color(white)(xxxxxxxxxxxxxxxxxx))(color(blue)(larr)# B
$\text{ "d_A" } {d}_{B}$

We use the fact that both runs share the same time t.

We have 3 unknowns and we can set up 3 simultaneous equations to solve them.

We know that average velocity = distance travelled / by the time taken.

${d}_{A}$ = distance travelled by A

${d}_{B}$ = distance travelled by B

$t$ is the time taken

$\stackrel{\rightarrow}{{V}_{A}} = {d}_{A} / t$

$\therefore 7 = {d}_{A} / t \text{ } \textcolor{red}{\left(1\right)}$

$\stackrel{\rightarrow}{{V}_{B}} = {d}_{B} / t$

$\therefore 6 = {d}_{B} / t \text{ } \textcolor{red}{\left(2\right)}$

and we know that:

${d}_{A} + {d}_{B} = 220 \text{ } \textcolor{red}{\left(3\right)}$

$\therefore {d}_{A} = \left(220 - {d}_{B}\right)$

Substituting this into $\textcolor{red}{\left(1\right)} \Rightarrow$

$7 = \frac{\left(220 - {d}_{B}\right)}{t} \text{ } \textcolor{red}{\left(4\right)}$

From $\textcolor{red}{\left(2\right)}$ we get ${d}_{B} = 6 t$

Substituting this into $\textcolor{red}{\left(4\right)} \Rightarrow$

$7 = \frac{\left(220 - 6 t\right)}{t}$

$\therefore 7 t = 220 - 6 t$

$t = \frac{220}{13} = 16.92 \textcolor{w h i t e}{x} s$

This is the time taken for the runners to meet.

Rearranging $\textcolor{red}{\left(1\right)} \Rightarrow$

${d}_{A} = 7 t$

${d}_{A} = 7 \times 16.92 = 118.46 \textcolor{w h i t e}{x} m$

This is the distance from point A where they meet.

Check the distance that B has run:

${d}_{B} = 220 - {d}_{A} = 220 - 118.46 = 101.53 \textcolor{w h i t e}{x} m$

As you would expect runner A covers more distance than runner B as he/she is running faster.