See if you can finish this rate problem in less than two minutes.
A transcontinental jet travels at a rate of x – 100 mph with a headwind and x + 100 mph with a tailwind between Wavetown and Urbanio, two cities 3,200 miles apart. If it takes the jet 2 hr 40 minutes longer to complete the trip with a headwind, then what is the jet’s rate flying with a tailwind?
(E) Cannot be determined by the information given.
Did you Plug in?
You may have been tempted to put together an algebraic equation. If you are adept at doing so, and can usually get the answer quickly, then I encourage you to go ahead and make an equation. Most students, however, find this strategy cumbersome and problematic. Even if they set up the right equation, which they can’t be quite sure of unless they get the answer, they may very well make a mistake in solving the equation. If this scenario describes what just happened when you attempted the problem above, know that there is a better strategy: Plugging-In.
When and Where to Plug-In
Once we’ve decided to plug in, where do we start? Do we plug in our own numbers, or the answer choices? First, we want to look at the answer choices. Are they numbers? If so, plug them in. If they are variables, you will need to come up with your own numbers, as long as those numbers conform to the information provided in the question.
Here we have answers, so let’s try plugging them in. The first place to start is the middle. The logic is if the number is too low (or too slow, in this case), you need to pick a larger number. Note: if the middle answer is a weird number like 625, then I would recommend plugging in (B) or (D).
Luckily, we can work with answer choice (C) 600. If the speed with a tailwind is 600 mph, then the speed with the headwind is 400. The distance between the two cities is 3200 miles. Using d = rt, where d stands for distance, r stands for rate, and t stands for time, we find that the time it takes to fly with a tailwind is 5 hr 20 min, and the time with a headwind is 8 hours. The difference in time is 2 hr 40 min. And there is our answer. Just like that.
If that seems too easy, that’s not a bad thing. Plugging-In can look like magic, in that it can make a seemingly intractable problem fall into place, just like that.