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

Answer:

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).