How do you solve this (math) word problem?

Question

In a recent year a baseball team paid six times as much to their ace pitcher as they paid to their shortstop. If they paid $42 million for the two salaries, what did they pay each player?

So, how do I find out

1. What was the pictures salary (millions of dollars)
2. What was the shortstop's salary?

Thanks.

Answer 1

Let S represent the shortstop's salary.
Therefore the pitcher's salary is 6S.
S + 6S = 42 million.
7S = 42
S = 6 million.
So the pitcher gets 36 million, the shortstop 6 million.

Answer 2

Answer: 1 + sqrt(2) miles Let s1 be the speed of the master ans s2 the speed of the train. The master and train travel in opposite directions until the master reaches the back of the train at time t1 at a distance d from the master's starting point. So, d = s1 * t1. The train's rear is d miles from the master's starting point, so the train's front must be at a distance of 1 - d miles from that point, which was also the train's starting point. The train has therefore traveled 1 - d miles, so 1 - d = s2 * t1. If we divide d by 1 - d we get d/(1-d) = s1/s2. Once the master reaches the end of the train, his horse does a piroette and he rides to the front of the train, reaching it as it hits the 1 mile mark. The train will have traveled distance d and the master distance 1 + d. So s1 * t2 = 1 + d and s2 * t2 = d. Division gives us s1/s2 = (1+d)/d. d/(1-d) = s1/s2 = (1+d)/d d^2 = 1 - d^2 2d^2 = 1 d^2 = 1/2 d = sqrt(2)/2 The master rode distance d, then 1 + d for a total of 1 + 2d = 1 + sqrt(2)