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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?

1 Answer

Oct 24, 2015

Kyle drove (approximately) $92.3$ $92.3$ km/hr

Explanation:

Let
$XXX S_{n} =$ $color(white)("XXX")S_n =$ speed at which Nadia drove (in km/hr)
$XXX S_{k} =$ $color(white)("XXX")S_k =$ speed at which Kyle drove (in km/hr)

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

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

The total distance driven was $1250$ $1250$ km
and therefore:
[1] $XXX 5 S_{n} + 8 S_{k} = 1250$ $color(white)("XXX")5S_n + 8S_k = 1250$

We are told
[2] $XXX S_{n} = S_{k} + 10$ $color(white)("XXX")S_n = S_k+10$

Substituting $(S_{k} + 10)$ $(S_k+10)$ from [2] for $S_{n}$ $S_n$ in [1]
[3] $XXX 5 (S_{k} + 10) + 8 S_{k} = 1250$ $color(white)("XXX")5(S_k+10)+8S_k=1250$

[4] $XXX 5 S_{k} + 50 + 8 S_{k} = 1250$ $color(white)("XXX")5S_k+50 + 8S_k = 1250$

[5] $XXX 13 S_{k} = 1200$ $color(white)("XXX")13S_k = 1200$

[6] $XXX S_{k} = \frac{1200}{13} ≅ 92.3$ $color(white)("XXX")S_k = 1200/13 ~= 92.3$

(The answer would have been "nicer" if Nadia had driven 10 km/hr slower than Kyle).

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