How do you solve this problem?

 The problem is:

‘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?’

This was considered to be one of the hardest questions from GCSE 2 years ago.Everytime we are given multiple information,it is a good idea to try to write what we know about each thing.

For example,we know that speed is distance over time. We note the distance from a to b with d and get :(notice that in this problem. speed is measured in km/h,time in hours and distance in km)

speed of Tom = d / t, so 90 = d/t, so by multiplying with t we get 90*t = d For Alice: 

speed of Alice = d/(t+1),so 70 = d/(t+1),so by multiplying with (t+1) we get 70*(t+1) = d.

As both are equal with d, we have the equality:

90*t=70*(t+1), so 90*t=70*t+70(by opening the parenthesis) .

If we subtract 70*t we get :

20*t=70,so by dividing with 20 we get :

t=70/20=3,5 hours, which is the value that we were asked about.

Marco-Iulian G. GCSE Maths tutor, Uni Admissions Test .MAT. tutor, A ...

1 year ago

Answered by Marco-Iulian, a GCSE Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


£20 /hr

Sara J.

Degree: Computing Science (Bachelors) - Glasgow University

Subjects offered:Maths, Geography+ 2 more

-Personal Statements-

“Undergraduate student at University of Glasgow with passion for Computing Science, Mathematics and Geography.”

£20 /hr

Ayyub A.

Degree: Mathematics Msci (Bachelors) - Bristol University

Subjects offered:Maths, Further Mathematics + 1 more

Further Mathematics

“Hi I'm Ayyub, current student at Bristol university studying Maths. I have significant tutoring experience in maths and hopefully i'll be able to help you out.”

£22 /hr

Runzhi C.

Degree: Medicine (Bachelors) - Imperial College London University

Subjects offered:Maths, Chemistry+ 3 more

-Personal Statements-
-Medical School Preparation-

“Hi there, I am a first year medical student at Imperial College London and I have lived in the UK all my life. I enjoy studying medicine because it encompasses both scientific knowledge and social aspects. I am relatively new to tutor...”

About the author

Marco-Iulian G. GCSE Maths tutor, Uni Admissions Test .MAT. tutor, A ...

Marco-Iulian G.

Currently unavailable: for regular students

Degree: Mathematics&Computer Science (Masters) - Bristol University

Subjects offered:Maths, Further Mathematics + 2 more

Further Mathematics

“I'm in my first year at University of Bristol, studying Mathematics and Computer Science MEng. From an early age I started to participate in lots of contests and maths olympiads, and the experience I achieved along the way enriched bo...”

You may also like...

Posts by Marco-Iulian

How can I find x and y?

How do I make calculations with percentages?

How do I solve a quadratic equation?

How do you solve this problem?

Other GCSE Maths questions

A right angled triangle with sides 7cm and 11cm, find the hypotenuse

At what points does the line y = x +1 intersect the circle x^2 + y^2 + 18x + 20y + 81 = 0.

Write the expression x^(2)+6x+2 in the form (x+a)^(2)+b where a and b are integers

Integrate ∫_(-1)^1 3/√(x+2) dx using the substitution u x+2

View GCSE Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss