Speed equals distance over time. Car A travelled twice the distance of car B. Car A travelled for half the time car B travelled. Complete the following sentence. The speed of car A was blank the speed of car B.
Let’s write out a formula for the speed of car A. The speed of car A equals the distance car A travelled over the time that car A travelled. We know that car A travelled twice the distance of car B. For the distance of car A, we can substitute two times the distance of car B. For the time that car A travelled, we can substitute half the time of car B, one-half times the time car B travelled.
We can do a little bit of simplification here. We could separate two over one-half. Two divided by one-half is the same thing as saying two times two over one, which equals four. If we plug the four in, then we see that the speed of car A is four times the distance of car B over the time of car B. And this value, the distance of car B over the time of car B, is the speed of which car B was travelling. Car A was travelling at four times the speed of car B.
Part b) of the question is about pressure. Pressure equals force over area. If the force is three times smaller and the area is doubled, what happens to the pressure? Circle the correct answer.
We have some pressure, and the force is three times smaller. Three times smaller is divided by three or multiplied by one-third, one-third of the force. And the area is changing by double. The area is being doubled, multiplied by two, two times the area.
Just like we did in the first part, we can break the fraction piece away from the force over area. One-third divided by two equals one-third times one-half, which is equal to one-sixth. We now have the pressure being equal to one-sixth times force over area.
We’ve already said that force over area equals pressure. These changes would take the original pressure and multiply it by one-sixth. And that’s the same as dividing the original pressure by six.