A train running between two towns arrives 10 minutes late with 40 miles per hour and 16 minutes late when it goes 30 miles per hour .what is the distance between these two towns ???

Question

please also write the whole solution with formula

Answer 1

Let t=normal time to travel between the two towns.

Distance, s=speed, v*time so although the distance doesn't change, the time does.

40 mph = 40/60 miles per minute=2/3; 30 mph = 30/60 mil per min = 1/2.

When the train is 10mins late we have the equations s=2(t+10)/3=(t+16)/2.

6s=4(t+10)=3(t+16), so 4t+40=3t+48, and t=8. Therefore, s=2*18/3=24/2=12 miles.

(The speed can also be calculated v=s/t=12/8=3/2mi/min=3/2*60=90mph.)