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\[\begin25t\ 20\left( \right)\end\] At this point a quick sketch of the situation is probably in order so we can see just what is going on.In the sketch we will assume that the two cars have traveled long enough so that they are 300 miles apart. That means that we can use the Pythagorean Theorem to say, \[ = \] This is a quadratic equation, but it is going to need some fairly heavy simplification before we can solve it so let’s do that.So, let’s convert to decimals and see what the solutions actually are.
Also, as the previous example has shown, when we get two real distinct solutions we will be able to eliminate one of them for physical reasons. We’ll start off by letting \(t\) be the amount of time that the first car, let’s call it car A, travels.
Since the second car, let’s call that car B, starts out two hours later then we know that it will travel for \(t - 2\) hours.
Statics can be applied to a variety of situations, ranging from raising a drawbridge to bad posture and back strain.
We begin with a discussion of problem-solving strategies specifically used for statics.
Also, even though the problem didn’t ask for it, the second car will have traveled for 8.09998 hours before they are 300 miles apart.
Notice as well that this is NOT the second solution without the negative this time, unlike the first example. Working together they can stuff a batch of envelopes in 2 hours.From the stand point of needing the dimensions of a field the negative solution doesn’t make any sense so we will ignore it. The width is 3 feet longer than this and so is 10.2892 feet. In this case this is more of a function of the problem.Notice that the width is almost the second solution to the quadratic equation. For a more complicated set up this will NOT happen. Due to the nature of the mathematics on this site it is best views in landscape mode.If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.Working separately, it will take the second machine 1 hour longer than the first machine to stuff a batch of envelopes.How long would it take each machine to stuff a batch of envelopes by themselves?Machine B will need 4.5616 hours to stuff a batch of envelopes by itself.Again, unlike the first example, note that the time for Machine B was NOT the second solution from the quadratic without the minus sign.\[\begin625 & = 90000\ 625 400 - 1600t 1600 & = 90000\ 1025 - 1600t - 88400 & = 0\end\] Now, the coefficients here are quite large, but that is just something that will happen fairly often with these problems so don’t worry about that.Using the quadratic formula (and simplifying that answer) gives, \[t = \frac = \frac = \frac\] Again, we have two solutions and we’re going to need to determine which one is the correct one, so let’s convert them to decimals.