lapsed time of two related events

Question

Hans and Freya are reading the same book. Freya reads one and a half times as fast as Hans. When Freya started reading, Hans had already read 36 pages. How many pages will each of them have read when Freya catches up with Hans?

Answer 1

Answer is 108 pages

F = 1.5H means Freya reads 1 1/2 times as fast as Hans

Hans started 36 pages ahead of Freya

when does Freya catch up to Hans?

F = H + 36, substitute 1.5H for F to get:

1.5H = H +36, solve for H

(1.5 - 1)H = 36

.5H = 36, multiply both sides by 2

H = 2(36) = 72 pages more for Hans, when Freya catches up

when Hans reads 72 pages more, Freya reads 1.5(72) = 108 pages

Hans previously read 36. Added to 72 more pages = 108 pages