Finding the speed of a person After hours of struggling I'm posting it here. I hope someone will solve it. > David and Jess start at the same time from points $A$ and $B$ and travel towards $B$ and $A$ respectively. After they meet, David takes $40$ minutes to reach $B$ and Jess takes $1.5$ hours to reach $A$. If David's speed is $36$ km/h, what is Jess's speed? My Work: if two people P and Q start at the same same time from A and B, after crossing each other they take X and Y seconds to reach B and A then P's speed : Q's speed = squareroot(y) : squareroot(x). i.e squareroot(1.5*60):squareroot(40) which is 3:2. so Jess's speed 36*2/3= 24Kmph. But i dont understand how P's speed : Q's speed = squareroot(y) : squareroot(x).

Let $S_D$ be Dave's speed, and $S_J$ be Jess's. Say they meet at time $t$ at distance $d_1$ from $A$ and $d_2$ from $B$. We can write $t=d_1/S_D$ and $t = d_2/S_J$ and combine them into $$\frac{d_1}{d_2} = \frac{S_D}{S_J}.$$

On the latter part of the journey, we can write similar equations $40=d_2/S_D$ and $90=d_1/S_J$ and combine these into

$$\frac{d_1}{d_2} = \frac{90S_J}{40S_D}.$$

Combining this with the equation above we get

$$90S_J^2 = 40S_D^2,$$

or $$S_J = \frac23 S_D.$$

$S_D = 36/60$ km/minute so $S_J=24/60$ km/minute, or $24$ kph.