Problema Solution
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 its new average speed?
Answer provided by our tutors
First I converted the 26 min to hours
26/60 = 0.433h
Here is the equation in terms of the old speed
(270mi / Xmph) - 0.433h = 270mi / (X + 4mph)
Multiply everything by X
270 - 0.433X = 270X / (X + 4)
Multiply everything by (X + 4)
270*(X + 4) - 0.433X*(X + 4) = 270X
Simplify
270X + 1080 - 0.433X2 - 1.732 = 270X
Subtract 270X from both sides
1080 - 0.433X2 -1.732 = 0
Combine like terms
1078.27 - 0.433X2 = 0
Subtract 0.433X2 from both sides
1078.27 = 0.433X2
Divide both sides bY 0.433
2490.23 = X2
Take the square root of both sides
49.9mi/h = X
Now remember that we solved for the old speed and that the new speed is 4mph faster
So the new speed is 53.9mph