# Nadia and Kyle shared the driving on a 1250- km trip from Edmonton to Vancouver.Nadia drove for 5 hours and Kyle drove for 8 hours.Nadia drove 10km/h faster than Kyle. How fast did Kyle drive?

Oct 24, 2015

Kyle drove (approximately) $92.3$ km/hr

#### Explanation:

Let
$\textcolor{w h i t e}{\text{XXX}} {S}_{n} =$ speed at which Nadia drove (in km/hr)
$\textcolor{w h i t e}{\text{XXX}} {S}_{k} =$ speed at which Kyle drove (in km/hr)

Since Nadia drove for 5 hours at a speed of ${S}_{n}$
she drove a distance of $5 {S}_{n}$ (km)

Since Kyle drove for 8 hours at a speed of ${S}_{k}$
he drove a distance of $8 {S}_{k}$ (km)

The total distance driven was $1250$ km
and therefore:
$\textcolor{w h i t e}{\text{XXX}} 5 {S}_{n} + 8 {S}_{k} = 1250$

We are told
$\textcolor{w h i t e}{\text{XXX}} {S}_{n} = {S}_{k} + 10$

Substituting $\left({S}_{k} + 10\right)$ from  for ${S}_{n}$ in 
$\textcolor{w h i t e}{\text{XXX}} 5 \left({S}_{k} + 10\right) + 8 {S}_{k} = 1250$

$\textcolor{w h i t e}{\text{XXX}} 5 {S}_{k} + 50 + 8 {S}_{k} = 1250$

$\textcolor{w h i t e}{\text{XXX}} 13 {S}_{k} = 1200$

$\textcolor{w h i t e}{\text{XXX}} {S}_{k} = \frac{1200}{13} \cong 92.3$