EDIT: SEE ROBERT J'S BETTER, MORE, EFFICIENT AND MORE INTUITIVE ANSWER ABOVE.
To read 70 pages has taken Sarah:
70 pages * (3 minutes / page ) = 210 minutes.
To read 30 pages has taken Henry:
30 pages* (4 minutes / 3 pages) = 40 minutes
This is THE STARTING POINT.
Sarah reads X more pages (total = 70+X) and Henry reads Y more pages (total = 30+Y). Once Henry catches up, they'll have each read a total of:
70 + X = 30 + Y. Simplifying (always do this when possible),
Y = X + 40.
We want to solve for either X or Y to tell us when they've read the same total number of pages. This is THE ENDING POINT.
Now, from THE STARTING POINT it will take the same amount of time
for each person to reach THE ENDING POINT. (Please ask if you don't understand why this must be true).
Sarah will have spent: X pages*(3 minutes / page) = 3X minutes
Henry will have spent: Y pages * (4 minutes / 3 pages) = (4/3)Y minutes
So, 3X = (4/3)Y. Simplifying,
Y = 9X/4
Now we have two equations, so we can solve for X or Y.
Y = X+40
Y = 9X/4
Here's how I did it:
X + 40 = 9X/4
4X + 160 = 9X
160 = 5X
X = 32
So Sarah (and Henry) will have read a total of 70 + (32) = 102 pages!
And, from THE STARTING POINT, it will have taken them an additional 3*(32) = 96 minutes.
Sarah has already read for 210 minutes, so she will have read for a total of:
210 + 96 = 306 minutes.
Henry has already read for 40 minutes, so he will have read for a total of:
40 + 96 = 136 minutes.