A word problem

Question

 A bus goes from town A to B in an exact time. If the bus goes at the rate of 50km/h, then it will arrive B 42min later than it had to and if it increases
its speed 5.5/9 m/sec., it will arrive B 30min earlier. Find:
A) The distance between the two towns;
B) The exact time that it takes to arrive town B
C) The speed of the bus(by schedule) for the exact time.

Answer 1

5.5/9 m/s= 5500/9(60)(60)= 55/54(9)= 55/486 = about 0.1132 km/hr saves 12 minutes = 12/60=1/5= .2 hour

.1132 x .2 = .02264 km from A to B

maybe think of it this way

you go 10 miles per hour in 2 hours, you went 10x2 = 20 miles. You go 50 mph, then go 60 mph an extra 10 mph and save 2 hours on your trip. You went 20 miles from A to B. Same math with saving 12 minutes by going 5.5/9 km/hr faster