Trains at each end of the 500 km long Eurotunnel under the E

Trains at each end of the 50.0 km long Eurotunnel under the English Channel start at the same time into the tunnel. Find their speeds if the train from france travels 8.0km/h faster than the train from England and they pass in 17.0 min.

Solution

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