SOLUTION: This problem says: Train A has a speed 15 miles per hour greater than that of train B. If train A travels 240 miles in the same time train B travels 195 miles, what are the speeds

Question 541066: This problem says:
Train A has a speed 15 miles per hour greater than that of train B. If train A travels 240 miles in the same time train B travels 195 miles, what are the speeds of the two trains?
There should be two answers, the MPH for train A and the MPH for train B.
I've looked through the applications chapter in my textbook and it is the most useless textbook ever, it doesn't even tell me how to do this problem. I'd really appreciate some insight on this problem,thank you
Found 2 solutions by scott8148, oberobic:
Answer by scott8148(6628) (Show Source):
You can put this solution on YOUR website!
"Train A has a speed 15 miles per hour greater than that of train B" ___ A = B + 15 ___ A - 15 = B

t = d / r ___ the times are the same (equal)

240 / A = 195 / B ___ 240 / A = 195 / (A - 15)

"cross" multiplying ___ 240A - 3600 = 195A ___ 45A = 3600

solve for A and then substitute back to find B

Answer by oberobic(2304) (Show Source):
You can put this solution on YOUR website!
Start with the basic distance equation: d = r*t, where d = distance, r = rate, and t = time.
.
Train A
r = x
d = 240 miles
t = 240/x
.
Train B
r = x-15
d = 195
t = 195/(x-15)
.
We are told the time for the trains is the same, so t=t.
.
240/x = 195/(x-15)
.
cross multiply
.
240*(x-15) = 195*x
.
240x -3600 = 195x
.
45x = 3600
.
x = 80 mph = speed of Train A
.
80-15 = 65 mph = speed of Train B
.
To check this answer, confirm that t for Train A = t for Train B.
240 miles/80 mph = 3 hr
195 miles/65 mph = 3 hr
Correct.
.
Answer: The speed of Train A is 80 mph. The speed of Train B is 65 mph.
.
Done.