One plane can travel 30 miles per hour faster than another. One of them goes 300 miles in the same time it takes the other to go 255 miles. What are their speeds?
A)190 mph; 220 mph
B)180 mph; 210 mph
C)170 mph; 200 mph
D)150 mph; 180 mph
E)200 mph; 230 mph

Question

Quizplus · Accepted Answer

Let's call the speed of the slower plane "x". Then the speed of the faster plane is "x+30". We know that the time it takes for each plane to travel their respective distances is the same. We can use the formula: Distance = Speed x Time. 
For the slower plane: 255 = x * t
For the faster plane: 300 = (x+30) * t
We can rearrange the first equation to solve for "t": t = 255/x. Then we can substitute that into the second equation: 300 = (x+30) * (255/x). 
Simplifying that, we get: 300 = 255 + 30(x/x) --> 45 = 30(x/x) --> x = 45. 
So the speed of the slower plane is 45 mph, and the speed of the faster plane is 75 mph (45+30). Thus the answer is C, 170 mph and 200 mph.

One Plane Can Travel 30 Miles Per Hour Faster Than