Today was the GCSE maths exam today. If you’re not based in the UK, GCSEs are the exams taken by students aged 15-16. Only if you complete your GCSEs can you go on to A Levels. If you can’t get an A in GCSE maths, you will probably never be an investment banker.

The exam was allegedly difficult. And this was allegedly the hardest question. Can you answer it? Can you answer it in two minutes maximum? Answers, and workings, in the comments box at the bottom of the page please.

*‘Tom travels from a to b and at a speed of 90km per hour. It takes him time ‘t’. Alice travels from a to b at a speed of 70km per hour. It takes her time ‘t+ 1 hour’.*

*How long did it take for Tom to complete his journey?’*

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## Comments (30)

t = 3.5 hours?

90t=70(t+1)

20t=70

t=70/20=3.5 hours

Tom total distance is 90t

Alice total distance is 70(t+1) = 70t +70

Thus 90t = 70t + 70, hence 20t = 70, thus t = 70/20 = 3.5hours

90km/h -> complete AB in time t

=> at 10km/h -> complete AB in 9t (it would take 9 times as long)

=> at 70km/h -> complete AB in 9t/7 (it would be 7 times quicker than at 10km/h)

at 70km/h, completed in time t + 1. t + 1 = 9t/7

7t + 7 = 9t

2t = 7, t = 3.5 hours. Tom completes in 3.5 hours

4.5 hours

speed = distance / time

as both travel the same distance, each speed times its required time would be equal to others

90t = 70 (t+1)

90t = 70t + 70

t = 3.5

Tom takes 3.5 hours

90t = 70(t+1)

t = 3.5

distance is same for both Tom and Alice, so u1t1=u2t2 , t2=t1+1 => u1t1-u2t1-u2=0 => t1(u1-u2)-u2=0 => t1=70/(90-70) => t1=3,5 hours

90-70=20 km/h different between Tom’s and Alice’s speed

and we know that time is different 1 hour

70/20=3.5 Alice’s time

3.5-1=2.5 Tom’s time

2.5 h

90-70=20 km/h different between Tom’s and Alice’s speed

and we know that time is different 1 hour

70/20=3.5 Alice’s time

3.5-1=2.5 Tom’s time

hi, I did the test today and I believe the answer is 4.5 hours as…..

90t-70t=20t

so 20t = the +1 on the 70 so,

20t=1hour

90/20=4.5hours

so tom takes 4.5 hours

(I think)

This was not the hardest on the paper, most people got this question as 3.5 hours, it was in the middle of the paper, the hardest was the question at the end, only a few answered both part (a) and part (b) correctly. You should have put that one up, unless you didn’t have access to the paper, and are in fact just using word of mouth, in which case, that’s not a basis to claim it is the hardest question on the paper, seeing as you are prevented from the use of diagrams.

And if I remember correctly it was only worth 2 or three marks out of the 70, so it wasn’t an important question, in terms of the whole paper.

If you are serious about this being the hardest question, it’s a disgrace to British math education. Seriously, this is a primary school level, what a waste of time “studying”. No wonder you can rarely find suitable locals to fill any analytic city positions.

I’m 16, having taken my GCSE maths exams a year early in June 2013 (achieving an A*) I can assure you that such a question is nowhere near the high end of the difficulty spectrum in GCSE maths exams.

All these answers are wrong as they ignore time dilation.

MEOW 3.5 HOURS

TMT THE MONEY TEAM

If this is the toughest Q then the maths std is very poor…

average speed=total distance/total time hence average speedxtotal time=total distance

90t=70(t+1) as distance travelled is the same

90t=70t+70

20t=70

t=3.5h

QED.

4.5

90t=70*(t+1)

solve T=3.5

Distance = speed*time

So

90t = 70(t + 1)

90t = 70t + 70

20t = 70

t = 3.5

Tom took 3.5 hours.

This took 10 seconds.

I study in an Indian school, and this is the kind of calculation our 5th graders excel at.

No, it is not 3.5 hours. It is 3 minutes and 30 seconds

90*t= 90t

t+1(70) = 70t+70

90t=70t+70

20t=70

t=3.5hours

just me is retarded

Speed=Distance/Time

70km=90t/t+1

70(t+1)=90t

70t+70=90t

20t=70

t=7/2 or 3.5

Takes tom 3.5 hours to get from A to B

GCSE for 15-16 years old will get impossible at 2017 and onwards. It will be impossible to get even B forget A or A*. Government need to change this.

Another perhaps simpler way of doing so:

Write all distances out,the answer is when the same number matches an hour later as shown below. This is also good as it shows you the distance between A and B rather than just the time

1. 1.5. 2. 2.5. 3. 3.5. 4. 4.5

Tom. 90. 135 180 225 270 (315)350 395

Alice. 70 105 140. 175 210 245 280 (315)

t=3.5 hrs. This comes no where near the hardest GCSE questions in England. And if you compare this level of ‘difficulty’ to the new 9-1 specification, this would be the easiest question on the exam paper.