Problem
Each member of a research group visited either the Virgin Islands or Hawaii...
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So What?
Math questions involving two equations and two unknowns can usually be combined into one equation with one unknown.
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SAT: Grid-In Question #10 |
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Question:
Caroline drove 50 miles to her mother's house at an average speed of 40 miles per hour, and she drove back on the same route at an average speed of 60 miles per hour. What was her average speed for the entire trip, in miles per hour?
Be careful: you can't just take the average of the two speeds, because Caroline will travel longer at the slower speed than she will at the faster speed. When you see a rate problem, you know you'll need to use the distance formula, which is distance = rate x time. The formula has three terms, and so if you know two of them, you can solve for the third term. Here, we're asked for Caroline's average speed, which means we're looking for the rate. So if we can figure out how far she traveled (distance) and how long she traveled (time), we can figure out the average speed (rate) at which she traveled.
| rate |
= |
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 |
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25 |
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12 |
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hours |
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| So how far did she travel? She went 50 miles one way and 50 |
| miles the other way. So she went a total of 100 miles. How long |
| did her trip take? This is the tough part, because we have to |
| use the distance formula to calculate the time each leg of her trip |
| Since distance |
= |
rate |
× |
time, the time each leg of her trip took |
| is equal to the distance traveled divided by her rate of speed. In |
| other words, since distance |
= |
rate |
× |
time, time |
= |
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distance |
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rate |
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. |
| Since we know the distance of each leg of Caroline's trip, and we |
| know her speed, we can calculate the time each leg of her trip |
| On the way to her mother's house, Caroline drives 50 miles at 40 |
| miles per hour, so she drives for |
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50 |
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40 |
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= |
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5 |
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4 |
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hours. On the way back, |
| she drives 50 miles at 60 miles per hour, so she drives for |
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50 |
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60 |
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= |
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5 |
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6 |
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hours. So it takes her |
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5 |
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4 |
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hours |
+ |
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5 |
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6 |
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hours |
= |
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15 |
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12 |
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hours |
+ |
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10 |
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12 |
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hours |
= |
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25 |
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12 |
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hours. |
| Now we have her distance (100 miles) and her time, |
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25 |
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12 |
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hours, |
| and so we can plug these into the distance formula to |
| Again, distance |
= |
rate |
× |
time, and so rate |
= |
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distance |
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time |
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. |
| So Caroline's average speed is: |
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