A car journey of 380 km lasts 4 hours. Part of this is on a motorway at an average speed of 110kmh^-1, the rest on country roads at an average speed of 70kmh^-1.
(i) Write this information as pair of simultaneous equations.
(ii) Solve you equations to find how many kilometres of the journey is spent on each type of road.
So, I know what the answers are but I can't figure out how to get to it myself. Please will you help by showing me how?
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use the relation v = d/t
v= speed , d = distance travel on a motorway and t = time taken on the motorway
so for motorway travel we have
110 = d/t
and for the country roads
70 = (380 - d) / (4 - t)
so there are your 2 equations
writing the equation without fractions we get
d = 110t
380 - d = 70(4 - t)
to solve for t
substitute d = 110t in the second equation
380 - 110t = 280 - 70t
380 - 280 = 110t - 70t
can you continue with this?