SOLUTION: Hi! Actually, I already knew the answer since I've searched it and found out a problem that's similar to my math problem. However, I didn't know how the answer was gotten. This is

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hi! Actually, I already knew the answer since I've searched it and found out a problem that's similar to my math problem. However, I didn't know how the answer was gotten. This is       Log On


   

Question 1094530: Hi! Actually, I already knew the answer since I've searched it and found out a problem that's similar to my math problem. However, I didn't know how the answer was gotten. This is also involved in physics with the formula of T = D/R (I'm not sure tho). Hoping someone would be able to teach me how. Thank you so much in advance! :)
Here's the question:
A car travels 500 miles in the same time that a train travels 300 miles. The speed of the car is 30 miles per hour faster than the speed of the train. Find the speed of the car and the train.
Found 2 solutions by greenestamps, josgarithmetic:
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!

The car travels 500 miles in the time the train travels 300 miles. Since the time is the same, the ratio of the speeds is the same as the ratio of the distances, 500:300, or 5:3.

Let the train's speed be x; then the car's speed is (5/3)x. Since we are also told that the car's speed is 30 mph faster than the train's speed,
%285%2F3%29x+=+x%2B30
%285%2F3%29x+=+%283%2F3%29x%2B30
%285%2F3%29x+-+%283%2F3%29x+=+30
%282%2F3%29x+=+30
x+=+30%283%2F2%29+=+45

The train's speed is 45 mph.
The car's speed is 45+30 = 75 mph.
or you can say the car's speed is (5/3)(45) = 75 mph.

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
            SPEED        TIME             DISTANCE

CAR         r+30         500%2F%28r%2B30%29        500

TRAIN       r            300%2Fr             300

Times are given as equal.
500%2F%28r%2B30%29=300%2Fr
-
5%2F%28r%2B30%29=3%2Fr

3r%2B90=5r

90=2r

highlight%28r=45%29-------speed of train