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Help with simultaneous equations

Can someone help me with this question?
A car journey of 380 km lasts 4 hours. Part of this is on a motorway at an average speed of 110 kmh^-1, the rest on country roads at an average speed of 70 kmh^-1.
i) write this information as a pair of simultaneous equations
ii) solve your equations to find how many kilometres of the journey is spent on each type of road.

I can do the maths side of it, but am really struggling to pick out the key information and put it in the correct places to make a pair of equations
any help greatly appreciated
Reply 1
Original post by aaustin2012
Can someone help me with this question?
A car journey of 380 km lasts 4 hours. Part of this is on a motorway at an average speed of 110 kmh^-1, the rest on country roads at an average speed of 70 kmh^-1.
i) write this information as a pair of simultaneous equations
ii) solve your equations to find how many kilometres of the journey is spent on each type of road.

I can do the maths side of it, but am really struggling to pick out the key information and put it in the correct places to make a pair of equations
any help greatly appreciated


I'll give it a try in explaining:

The questions states that the car travelled an average of 110kmh for an unknown distance of lets say X. It also states that it travelled a speed of 70kmh for another unknown distance Y.

Overall you'll have 110X + 70Y = 380.

Here's a super hint: use distance = speed x time for the second question.
Reply 2
Original post by aaustin2012
Can someone help me with this question?
A car journey of 380 km lasts 4 hours. Part of this is on a motorway at an average speed of 110 kmh^-1, the rest on country roads at an average speed of 70 kmh^-1.
i) write this information as a pair of simultaneous equations
ii) solve your equations to find how many kilometres of the journey is spent on each type of road.

I can do the maths side of it, but am really struggling to pick out the key information and put it in the correct places to make a pair of equations
any help greatly appreciated


Let xx be the time driven at 110kmh1110 kmh^{-1} and yy be the time driven at 70kmh170kmh^{-1}
What can you tell me about the total time x+yx+y?
How can you use the 380km380km distance?
Reply 3
Original post by aaustin2012
Can someone help me with this question?
A car journey of 380 km lasts 4 hours. Part of this is on a motorway at an average speed of 110 kmh^-1, the rest on country roads at an average speed of 70 kmh^-1.
i) write this information as a pair of simultaneous equations
ii) solve your equations to find how many kilometres of the journey is spent on each type of road.

I can do the maths side of it, but am really struggling to pick out the key information and put it in the correct places to make a pair of equations
any help greatly appreciated


distance = speed x time

the unknowns will be t1 and t2

any good?
Reply 4
I can get that bit, but they are not simultaneous equations, i cannot figure out how to write as a pair of equations
Reply 5
Original post by aaustin2012
I can get that bit, but they are not simultaneous equations, i cannot figure out how to write as a pair of equations


You have both the time taken to get to the destination - 4 hours, and the distance between the two places 380km.
You also know the speeds. Can you construct 2 equations, one for the time, and another for the distance traveled in terms of two unknowns?

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