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Can you answer the hardest question from the GCSE maths exam?


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 (32)

  1. t = 3.5 hours?

  2. 90t=70(t+1)


    t=70/20=3.5 hours

  3. 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

  4. 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

  5. 4.5 hours

  6. 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

  7. 90t = 70(t+1)
    t = 3.5

  8. 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

  9. 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

  10. 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

  11. hi, I did the test today and I believe the answer is 4.5 hours as…..
    so 20t = the +1 on the 70 so,
    so tom takes 4.5 hours
    (I think)

  12. 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.

  13. 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.

  14. 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.

    AlexanderOrlov Reply
  15. 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.

  16. All these answers are wrong as they ignore time dilation.

  17. MEOW 3.5 HOURS


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

  19. average speed=total distance/total time hence average speedxtotal time=total distance
    90t=70(t+1) as distance travelled is the same

  20. 4.5

    123456ertyxcvbnm Reply
  21. 90t=70*(t+1)

    solve T=3.5

  22. Distance = speed*time
    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.

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

  24. 90*t= 90t
    t+1(70) = 70t+70

  25. just me is retarded

  26. Speed=Distance/Time

    t=7/2 or 3.5
    Takes tom 3.5 hours to get from A to B

  27. 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.

  28. 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)

  29. 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.

  30. I’m a GCSE Student and found this no way near difficult.
    S1 = 90km/h
    T1 = ?
    D1 = 90 * T1

    S2 = 70km/h
    T2 = T1 + 1
    D2 = 70(T1 + 1) = 70T1 + 70

    If they take the same route then D1 = D2 Lets assume x = T1 Now
    90x = 70x + 70
    20x = 70
    x = 70/20 = 7/2 = 3.5
    x is hours as its km/h
    3.5 hours = 3 hours 30 minutes :)
    For all you guys who said 3.5 hours OR 3 hours 30 mins, You’re correct.

    Year 10 GCSE Student Of 2018 Reply
  31. hi, I just had a go at this question and I found out that the answer is 3.5 as Alice took (t + 1) hour and Tom took t hours all you had to do was skim the takes and get the important numbers you need for the sum which were 70 and 20. to work out how long t was all you had to do was figure out how to get to 70 from 20 which gives you the answer of 3.5 thus t equals
    and I’m not even doing my gcse yet

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