Q: A new schedule for a train requires it to go 270 miles in 26 minutes less time than before. To do this it must average 4 miles per hour faster. What must be it's new average speed?

A: Let the old average speed of the train be x miles/hr. With this speed the train covers 270 miles in (270/x) hr.

Thus, new average speed of that train is (x+4) miles/hr. so that the the train now covers 270 miles in (270/(x+4)) hr.

By the condition of the problem,

(270/(x+4)) = (270/x) - 26/60, since 26 mins = 26/60 hr.

or, 270/(x+4) = [270 X 30 - 13x]/30x

or, 13x2+52x-270 X 30 X 4=0

or, x = (2/13) (-13-sqrt(105469)), (2/13) (-13+sqrt(105469)).

Since x is a measure of speed, it cannot be negative. Thus, x = (2/13) (-13+sqrt(105469)) = 47.9631

Therefore, the new average speed x+4 = 51.9631 miles/hr.