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Kasturi K.

Neuroscience student at the University of Texas at Austin

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Question:

If an object travels at 6 feet per second, how many feet will it travel in 2 hours?

Kasturi K.

Answer:

We are given the speed of an object (6 ft/sec) and time (2 hours). Our time is given in hours, but our speed is given in feet/seconds. We need to convert the hours to seconds, so that it will cancel out with feet/seconds and we will be left with an answer in units of feet. Let's start with 2 hours. We know that there are 60 minutes in an hour, and 60 seconds in a minute. Thus, we can multiply by conversion factors like this: 2 hours x (60 minutes/1 hour) x (60 seconds/1 minute) = 7200 seconds As you can see, the hours and minutes cancel each other out because they exist in the numerator and denominator. Now that we have converted the time to seconds, we can multiply this by the given speed. 7200 seconds x 6 feet/seconds = 43200 feet The object will travel 43,200 feet in 2 hours.

Basic Math

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Question:

What is half of one half equal to?

Kasturi K.

Answer:

When a question asks for half of something, it means we are dividing by two. So, when the questions asks for a half of one half, we can write it as: (1/2)/2 The rule for dividing two fractions is to flip the second one (switch the numerator and denominator) and then multiply the two fractions. So, if we think of the 2 in the denominator as 2/1 (because anything divided by one is itself), when we flip it, we get 1/2. Thus, we end up multiplying these two fractions: 1/2 x 1/2 As you multiply the numerators and denominators separately, you end up with 1/4 as your answer. Another way of visualizing this is to look at half of a pie. If you cut this half a pie in half, you are left with two quarters of a pie. Thus, a half of a half is a quarter, or 1/4.

Algebra

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Question:

After grading the students' recent tests, a teacher found that the highest grade was 48 points higher than the lowest grade. The sum of these two grades was 144. Find the lowest grade.

Kasturi K.

Answer:

We have two unknowns; the highest grade and lowest grade. We must start by assigning these values variables. 1) Let L = the lowest grade, and H = the highest grade. Next, we are told that the highest grade was 48 points higher than the lowest grade. We are also told that the sum of the two grades is 144. These can be written as equations using the variables we have assigned. 2) H = L + 48 L + H = 144 The first equation gives the value of H. Thus, (L + 48) can be substituted for H in the second equation. This is how we get rid of H; now, we only have to solve for L, the variable we were looking for in the first place. 4) L + (L + 48) = 144 2L +48 = 144 Subtract 48 from both sides, then divide both sides by 2, to isolate L. 5) 2L = 96 L = 48 The lowest grade was 48.

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