Here in this example question it says if 50g block of lead at 250�C it's submerged in a solution at 90�C the final temperature of the solution will be. So let's just think about it. We have a container. We have a hot piece of lead here being submerged in some colder water. So try to use everyday real experiences here. What happens?
I take a hot pan and I dunk it into the sink filled with water. We'll hear the pan sizzle. That's because the pan is releasing its extra heat into the water. The water is becoming vaporized. Remember, at thermal equilibrium, they're both going to reach a temperature that's the same for both of them.
The temperature that they reach should be a temperature somewhere between 150�C and 90�C, because we'd expect the hotter object to release enough heat so that it and the solvent that it's in can reach the same temperature. So the hotter object cools down some, the colder object warms up some. Their new final temperature will exist somewhere between their two initial temperatures, so we'd expect that the temperature of the solution to be greater than 90�C. It'll be a number between 150 and 90�C.