an aeroplane flies 3500km in the same time a train covers 600 km . if the speed of the aeroplane is five times the speed of the train . what are the speeds of the train and aeroplane ?

rosala
May 23, 2014

#3**+8 **

Hi Rosala,

Let the time travelled be T hours

Plane: 3500km in T hours so $$speed=\frac{3500}{T}\:km/hour$$

Train: 600km in T hours so $$speed=\frac{600}{T}\:km/hour$$

5 times speed of train = $$\frac{5*600}{T}=\frac{3000}{T}\:km/hour$$

Speed of plane = $$\left(\frac{3000}{T}+50\right)km/hour$$

so $$speed=\frac{3500}{T}\:km/hour$$ = $$\left(\frac{3000}{T}+50\right)km/hour$$

$$\begin{array}{rll}

\frac{3500}{T}&=&\left(\frac{3000}{T}+50\right)\\\\

T\times\frac{3500}{T}&=&T\times\left(\frac{3000}{T}+50\right)\\\\

3500&=&3000+50T\\\\

500&=&50T\\\\

T&=&10

\end{array}$$

Plane speed = 3500/10 = 350km/hour

Train speed = 600/10 = 60 km/hour

You should check that these answers make the word problem correct!

Melody
May 24, 2014

#1**+8 **

That appears to be impossible, rosala

If the speed of the airplane is five times that of the train, it would travel 5 times as far in the same time

But 3500 / 600 = about 5.8 times as far

CPhill
May 23, 2014

#2**+3 **

im sorry everyone mistakenly i missed out a part of the question heres th correct question ;

an aeroplane flies 3500km in the same time a train covers 600 km . if the speed of the aeroplane is 50km/hr more than five times the speed of the train . what are the speeds of the train and aeroplane ?

rosala
May 23, 2014

#3**+8 **

Best Answer

Hi Rosala,

Let the time travelled be T hours

Plane: 3500km in T hours so $$speed=\frac{3500}{T}\:km/hour$$

Train: 600km in T hours so $$speed=\frac{600}{T}\:km/hour$$

5 times speed of train = $$\frac{5*600}{T}=\frac{3000}{T}\:km/hour$$

Speed of plane = $$\left(\frac{3000}{T}+50\right)km/hour$$

so $$speed=\frac{3500}{T}\:km/hour$$ = $$\left(\frac{3000}{T}+50\right)km/hour$$

$$\begin{array}{rll}

\frac{3500}{T}&=&\left(\frac{3000}{T}+50\right)\\\\

T\times\frac{3500}{T}&=&T\times\left(\frac{3000}{T}+50\right)\\\\

3500&=&3000+50T\\\\

500&=&50T\\\\

T&=&10

\end{array}$$

Plane speed = 3500/10 = 350km/hour

Train speed = 600/10 = 60 km/hour

You should check that these answers make the word problem correct!

Melody
May 24, 2014

#5**+3 **

Do you mean this bit?

$$\begin{array}{rll}

\frac{3500}{T}&=&\left(\frac{3000}{T}+50\right)\\\\

T\times\frac{3500}{T}&=&T\times\left(\frac{3000}{T}+50\right)\\\\

\end{array}$$

I multipled both sides by T so that I could get the T off the bottom.

See, the next line just becomes this;

$$\begin{array}{rll}

3500&=&3000+50T\\\\

\end{array}$$

Because the Ts cancelled out

I'll put in a bit more working to show you.

$$\begin{array}{rll}

\frac{3500}{T}&=&\left(\frac{3000}{T}+50\right)\\\\

T\times\frac{3500}{T}&=&T\times\left(\frac{3000}{T}+50\right)\\\\

\frac{3500\times T}{T}&=&\frac{3000\times T}{T}+50\times T\\\\

3500&=&3000+50T\\\\

500&=&50T\\\\

T&=&10

\end{array}$$

If you still do not understand let me know. Also tell me if it is still the same spot that is causing you problems because I already have ideas on how I can help you understand. Just think about it for a little while first though.

Melody
May 24, 2014

#6**+3 **

could u just tell me the reason for ur steps that u are doing ! im sure after this ill understand this ques. very nicely

rosala
May 24, 2014

#7**+3 **

Okay Rosala,

I am going to try something different and ask you some questions!

How do you solve this equation? Remember, you need to get the X off the bottom and you need to do the same thing to both sides to keep it 'balanced'

1) $$5=\frac{6}{X}$$

Think about it and if you don't know - say so!

Melody
May 25, 2014

#9**+3 **

Not quite rosala.

If 5=6/x, multiply both sides by x to get 5x = 6.

Now ** divide** both sides by 5 to get x = 6/5 (or x = 1.2)

Do it one step at a time.

Alan
May 25, 2014

#10**+3 **

Okay Rosala

Now I have identified some of your problems. You cannot do equations because there are earlier concepts that you need to understand first!

I would like you to work through this unit.

http://www.mathsisfun.com/fractions_multiplication.html

Whenever anyone teaches antthing there are always slightly different methods.

I have not completely worked through the unit that I have sent you to (I think it wil be a good unit) but i did spot one thing I would do differently.

When you multiply with fractions, both numbers must be in fraction form so

$$6\times\frac{5}{3}

=\frac{6}{1}\times\frac{5}{6}$$

See, the 6 was not a fraction - But 6 over 1, (which is 6 divided by 1) is the same thing. and now it is in fraction form.

In the unit they put the 6 on top of a fraction line but they do not put the one underneath. I want you to put the one there like i have in my example.

Now the 6 on the top can be cancelled with the 6 on the bottom.

Try working through the unit. If you have problems with the unit let me know.

When you have finished also let me know. And we will move on from there.

I would also like you to tell me what you think of the unit because I often send people to sites like this and I do not get much feedback so i do not know how good they are.

Thank you Rosala.

Melody
May 26, 2014