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 Answer: The speed of the slower train is 34 mph.
