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.**

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