Question 68402

Let x=English train's speed
Then x+8=French train's speed

Distance(d)=rate(r) times time(t) or d=rt 

17 min=17/60 hr

Distance English train travels in 17 min =x(17/60) km
Distance French train travels in 17 min =(x+8)(17/60) km

Now when the sum of these distances equals 50 km, then the trains will be together.  So our equation to solve is

x(17/60)+(x+8)(17/60)=50  multiply through by 60 to clear fractions

17x+17(x+8)=3000 clear parens
17x+17x+136=3000 subtract 136 from both sides

34x=3000-136
34x=2864
x=84.235 km/hr--------------------------------speed of English train

x+8=84.235+8=92.235 km/hr-----------------------speed of French train


ck

distance English train travels in 17 min =84.235(17/60)=23.867 km
distance French train travels in 17 min =92.235(17/60)=26.133km
Now if we subtract either of these distances from 50 km we should get the other distance. 50-26.133=23.867  and 50-23.867=26.133

Hope this helps---ptaylor