How do you solve this problem?

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 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.

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