a train covered 120 miles at a certian speed. Had the train had been able to travel 10 miles per hour faster, the trip would have been 2 hours shorter. how fast did the train go
What Peritus did was use a simple $\displaystyle Time=\frac{Distance}{Velocity}$ forumula
Distance=D=120 in miles
Veolicty=V in miles/hours
Time=T hours
So for the first train
$\displaystyle T=\frac{120}{V}$
For the second train Velocity is increased by 10 and time is decreased by 2 hours. So
$\displaystyle T-2=\frac{120}{V+10}$
$\displaystyle T=\frac{120}{V+10}+2=\frac{120}{V}$
Then just solve for V.
It will be a quadratic giving you -30 and 20 but -30 is inadmisable because the train would be traveling backwards so your answer is V=20miles per hours
case 1
LEt the distance covered = 120
let x be the speed of the train and let y be the time taken
Speed=distance/time
x=120/y
so xy = 120 ------------------> equation 1
case 2
If the train traveled 10 mph faster then time is reduced by 2 hours
so x+10 = 120/y-2
(x+10)(y-2) = 120
multiplying we get
xy -2x +10y -20 = 120
from equation 1,
120 - 2x + 10y - 20 = 120
subtracting 120 on both sides
-2x + 10y -20 = 0
so x = (10y - 20)/2
x = 5y - 10
substituting this in equation 1 we get
(5y-10)y = 120
5y^2 -10y - 120 = 0
so now its a quadratic equation, we see that 5 is common on both sides so we divede 5 on both sides
y^2 -2y - 24 = 0
factorizing we get
(y+4)(y-6) = 0
so either y= -4 or y = 6
but time can't be negative so we conclude that the time taken is 6 hours, substituting this in equation 1 we get x = 120/6
x = 20 mph
so the train was traveling at 20 mph, it's so slow, you can use the bus
Regards,
Ice Sync