Snowboarding cautiously down a steep slope at a speed of 5.3 m/sec, sarah, whose mass is 53.0 kilograms, is afraid she won't have enough speed to travel up a slight uphill grade ahead of her. she extends her hand as her friend trevor, having a mass of 100 kilograms is about to pass her traveling at 16 m/sec. if trevor grabs her hand, calculate the speed at which the friends will be sliding.

We can consider each friend as a particle, with mass m1 and m2. 

Let us also say that the velocity at which each friend travels is v1 and v2

If we consider the conservation of the total momentum, (with momentum defined as the mass times velocity, P = m. V) 

m1 * v1 + m2 * v2 = (m1 + m2) * Vf 

Here we add the masses 1 and 2 because Sarah and Trevor are sliding together.

so with m1 = 53kg , m2 = 100kg , v1 = 5.3m/s , v2 = 16m/s,

We can obtain Vf which is equal to 12,29 m/s