Distance problem - aptitude Tim and Elan are 90 km from each other.they start to move each other simultanously tim at speed 10 and elan 5 kmph. If every hour they double their speed what is the distance that Tim will pass until he meet Elan. If we draw it on a scale, Tim goes 10, 30, 70...while Elan goes 85, 75, 55... Options are 60, 30, 80 and 45.

Doubling each speed is the same as doubling the relative velocity. The relative velocity starts at $15$, so the next hour it will be $30$, and the next $60$.

Since we want $90$ to be traveled between the both of them, we know it's after $2$ hours ($45 km$) and before $3$ ($105$ km). So after $2$ hours, they have $45$ km left to go, traveling at $60$ km/hr. So they meet at $2$ hours, $45$ minutes.

So if we want to find the distance traveled by Tim, we have his first speed*$1$ hr plus his second speed*$1$ hr plus the his third speed times $.75$ of an hour. So $10+20+40(.75)=60$ km.