The difference in the average speed of two trains is 16 miles per hour. the slower train takes 2 hours longer to travel 170 miles than the faster train takes to travel 150 miles. find the speed of the slower train.

Lets assume that s is the speed of the slower train and f is the speed of the faster train.
s = f - 16
f = 150 / t
s = 170 / ( t+2 )

170 / ( t+2 ) = 150 / t  - 16  / t * ( t + 2 ) 
170 t = 150 * ( t + 2 ) - 16 t * ( t + 2 )
170 t = 150 t + 300 - 16 t² - 32 t
16 f² + 52 t - 300 = 0 /  : 4  ( We will divide both sides of the equation by 4 )
4 t² + 13 t - 75 = 0
t 1/2 = ( -13 + √(169 + 1200 ) )/ 8
t = ( - 13 + 37 ) / 8 = 24 / 8 = 3
t = 3 h
s = 170 : ( 3 + 2 ) = 170 : 5 = 34 mph
The speed of the slower train is 34 mph.

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