2 trains depart from opposite directions at depots 172 miles apart.

The fastest left 20 minutes sooner traveling 6 mph faster than the 2nd train. The two trains pass each other 3 hr after the slower train left its depot. What is the faster train's speed? (The answer is 30. I don't see how.)

LET THE SPEED OF FASTER TRAIN BE X MPH

SPEED OF SLOWER TRAIN = (X -6) MPH

IN 20 MINUTES THE FASTER TRAIN HAS ALREADY TRAVELED X /3 MILES

DISTANCE REMAINING = (172 - X /3 ) MILES

TIME TAKEN TO MEET = 3 HOURS

NETT SPEED = X + X -6 = (2X -6) MPH

(172 - X/3 ) / ( 2X -6 ) = 3

3 ( 2X -6) = 172 - X/3

6X -18 = 172 -X/3

6X + X/3 = 172 +18 = 190

19/3 X = 190

X = 190 x3/19 = 30 MPH ANSWER

CHECK
FAST TRAIN
30 x 3 = 90 MILES
30 x 1/3 = 10 MILES
24 x 3 = 72 MILES
TOTAL = 172 MILES