Question 193131
Let x=no of hours it takes for the local train
x-1=no of hours it takes for the express train
.
Since speed=distance/time,
speed of the local train = 50/x
speed of the express train =50/(x-1)
If the express train is twice as fast as the local train then:
{{{2*(50/x)=50/(x-1)}}}
{{{100/x=50/(x-1)}}}
Multiplying both sides by x*(x-1), we get:
{{{100*(x-1)=50*x}}}
{{{100x-100=50x}}}
Subtracting 50x from both sides, we get:
{{{50x-100=0}}}
Adding 100 on both sides, we get:
{{{50x=100}}}
Diving both sides by 50 we get:
x=2
So, the local train takes 2 hours to get to Chicago and the express only takes 1 hour to get there.
speed of the local train = 50/2 = 25 mph
speed of the express train = 50/1 = 50 mph