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 90t = 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:
90t=70(t+1), so 90t=70t+70(by opening the parenthesis) .
If we subtract 70t we get :
20t=70,so by dividing with 20 we get :
t=70/20=3,5 hours, which is the value that we were asked about.