Question

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?

Answer 1

Kyle drove (approximately) `92.3` km/hr

Explanation:

Let
`color(white)("XXX")S_n =` speed at which Nadia drove (in km/hr)
`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`
she drove a distance of `5S_n` (km)

Since Kyle drove for 8 hours at a speed of `S_k`
he drove a distance of `8S_k` (km)

The total distance driven was `1250` km
and therefore:
[1]`color(white)("XXX")5S_n + 8S_k = 1250`

We are told
[2]`color(white)("XXX")S_n = S_k+10`

Substituting `(S_k+10)` from [2] for `S_n` in [1]
[3]`color(white)("XXX")5(S_k+10)+8S_k=1250`

[4]`color(white)("XXX")5S_k+50 + 8S_k = 1250`

[5]`color(white)("XXX")13S_k = 1200`

[6]`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).