The distance between towns A and B is 300 km. One train departs from town A and another train departs from town B, both leaving at the same moment of time and heading towards each other. We know that one of them is 10 km/hr faster than the other. Find the speeds of both trains if 2 hours after their departure the distance between them is 40 km.
Choose the correct choice:
A) 22  B) 27  C) 236  D) 90  E) 81
Let the speed of the slower train be xx km/hr. Then the speed of the faster train is (x+10)(x+10) km/hr. In 2 hours they cover 2x2x km and 2(x+10)2(x+10)km, respectively. Therefore if they didn't meet yet, the whole distance from A to B is 2x+2(x+10)+40=4x+602x+2(x+10)+40=4x+60 km. However, if they already met and continued to move, the distance would be 2x+2(x+10)−40=4x−202x+2(x+10)−40=4x−20km. So we get the following equations:   4x+60=3004x+60=300   4x=2404x=240   x=60x=60 or   4x−20=3004x−20=300   4x=3204x=320   x=80x=80   Hence the speed of the slower train is 60 km/hr or 80 km/hr and the speed of the faster train is 70 km/hr or 90 km/hr.   Answer:90
<result>D</result>
The distance between towns A and B is 300 km. One train departs from town A and another train departs from town B, both leaving at the same moment of time and heading towards each other. We know that one of them is 10 km/hr faster than the other. Find the speeds of both trains if 2 hours after their departure the distance between them is 40 km.