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- anonymous

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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- welshfella

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)

- welshfella

so there are your 2 equations

- welshfella

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?

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- welshfella

oh they want number of kilometers on each type of road
I should have solved for d
no matter when we find t we can then plug in the values to find the distances

- welshfella

fo you follow it OK so far?

- welshfella

are you there?

- anonymous

Yes, I am just a bit confused since those are not the answers my book got? I will give those too you now...

- anonymous

t(subscript 1) + t(subscript 2) =4;
110t(subscript 1) + 70t(subscript 2) = 380
Sorry I cant type the subscript numbers on my computer.

- anonymous

That is what my textbook has said are the answers to the first question.

- welshfella

yes thats basically the same as i have bu they have called the two times t1 and t2
whereas ive called them t and 4 - t because total time was 4 hours

- welshfella

if you solve for t you;ll find t = time for motoirway journey = 2.5 hours and so time foe road journey = 4-2.5 = 1.5
and distance for motorway = 110 * 2.5 = 275km
and for raoad = 70 8 1.5 = 105 km

- welshfella

t1 + t1 = 4
110 t1 + 70 t2 = 380
is what your book has said

- welshfella

do you want me to show you how to solve this?

- welshfella

there is often a few different ways to solve problems like this.

- anonymous

Oh ok. I think I understand now- thank you very much!

- welshfella

oh that should be t1 + t2 = 4

- welshfella

yw

- welshfella

t1 being time for motorway and t2 time for roads

- anonymous

Ok. You have helped me a lot!

- welshfella

yw

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