Yr 7 maths questions - compound measures

[LeggyMeggy]

Hi, would really love some help with this question, the simple compound equations are fine but seemingly there are two unknowns here - distance and time. And there's duplication in the multiple choice answers so that's throwing my child too. Any help on method would be hugely appreciated!

Driving to Birmingham airport, Mary cruised at 55 miles per hour for the first two hours and then flew along at 70 miles per hour for the remainder of the journey. Her average speed for the entire journey was 60 miles per hour. How long did Mary’s journey to Birmingham Airport take?

A 6 hours B 4 hours C 4 hours D 3 hours E 3 hours

Maths teacher here.

Done it - but hard q! What age group?

The key is the total average speed is 60.

So 55mphx2hrs + 70mphx?hrs all divided by 2hrs+?hrs = 60

So 110 + 70x / 2+X = 60

Working this out gives X=1.
This means they travelled for 1 hr at 70mph.

Checking...
Speed = d/t

Total distance = 110+70
Total time = 3hrs

So speed = 180/3 = 60

Does that help?

I think I love you! Thank you SO much. Year 7, top set but still, seems a bit much. There are more like it but your extremely clear working out has saved me.

Sending you virtual 🍷

No problem at all!
That is fairly challenging for Yr 7.. but sometimes a challenge is good.

I enjoyed it!

In year 7 I'd expect them to do it by reasoning rather than algebra.

Try 1 hour at 70mph first..
55 + 55 + 70 = 180mph do average speed = 180/3 = 60mph.

This is right so the total journey time is 2hrs at 55mph plus 1 hour at 70mph so 3 hours together.

That's how I was looking at it but they're also doing equation of a gradient and other quite complicated algebraic calculations and the expectation is to show working rather than reasoning.

Frankly I'm quite terrified that I'm struggling to help with Year 7. God help us by Year 9!