SOLUTION: An aeroplane flies 3500 km in the same time a train covers 600 km.If the speed of the aeroplane is 50 km/h more than five times the speed of the train ,what are the speeds of the t

Question 979070: An aeroplane flies 3500 km in the same time a train covers 600 km.If the speed of the aeroplane is 50 km/h more than five times the speed of the train ,what are the speeds of the train and the aeroplane?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
rate * t = distance
rt = d
for the plane:
rt = d becomes rt = 3500
for the train:
rt = d becomes rt = 600
since the time each takes is the same, we'll solve for t.
for the plane, t = d/r = 3500/r
for the train, t = d/r = 600/r
since t is the same for each, then t = t, or their equivalents:
3500/r = 600/r
the rates are different, so we'll need to distinguish beween the two rates.
we'll call r for the plane r1.
we'll call r for the train r2.
the equation becomes:
3500/r1 = 600/r2
we are told that the plan travels 5 times as fast as the train plus 50 km/hr.
the equation for that is:
r1 = 5r2 + 50
we'll replace r1 with 5r2 + 50 in the equation of 3500/r1 = 600/r2 to get:
3500 / (5r2+50) = 600 / r2
we'll cross multiply to get:
3500 * r2 = 600 * (5r2 + 50)
simplify to get:
3500r2 = 3000r2 + 30000
subtract 3000r2 from both sides of this equation to get:
500r2 = 30000
solve for r2 to get:
r2 = 60
since r1 = 5r2 + 50, this means that r1 = 350.
the train travels at 60 kmph.
the plan travels at 350kmph.
now that we know the rates and distance, we can solve for time.
for the plane:
350*t = 3500
solve for t to get t = 10 hours.
for the train:
60*t = 600
solve for t to get 10 hours.
the time for both is 10 hours as it should be since they both took the same amount of time.
this confirms our calculations are correct.
our solution is:
the plane travels at 350kmph
the train travels at 60kmph
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