A train travels 100 km in the same time that a plane covers 450 km. If the speed of the plane is 30 km per hr less than 5 times the speed of the train, find both speeds.
Step 1
let
train
distance= 100 km
time= t1
speed=S1
plane
If the speed of the plane is 30 km per hr less than 5 times the speed of the train,in math terms it is,
speed2=(5*S1)-30
time=t1 ( the same time)
distance=450 km
Step 2
the time is given by
[tex]\text{time}=\frac{dis\tan ce}{\text{speed}}[/tex][tex]\begin{gathered} \text{from train} \\ t=\frac{100}{S1} \\ \text{from plane} \\ t=\frac{450}{(5\cdot S1)-30} \\ t=t,\text{ so} \\ \frac{100}{S1}=\frac{450}{(5\cdot S1)-30} \\ 100(5S1-30)=450S1 \\ 500S1-3000=450S1 \\ 500S1-450S1=3000 \\ 50S1=3000 \\ S1=\frac{3000}{50} \\ S1=60 \end{gathered}[/tex]
Now, S2
[tex]\begin{gathered} \text{Speed}2=5\cdot s1-30 \\ \text{speed}2=5\cdot60-30 \\ \text{speed}2=300-30 \\ \text{speed}2=270 \end{gathered}[/tex]
so, the speed of the train is 60 Kph and speed of planes is 270 kph
