Aptitude - Time and Distance - Discussion

How can we add. Minutes to the hours like 200 hours and 30 minutes.

Let the speed be 'S' kmph and time 't' hr.

So S = 600/t --- (1).

And since speed got reduced by 200 and time increased but 30 min.

So (s - 200) = 600/ (t + 30/60) --- (2).

Solving 1 and 2 equation we will get:

2t^2 + t-3 = 0 --- (3).

By equation 3 we will get:

t = -3/2 or t = 1/2.

Since time can't be negative. So t = 1/2.

Putting this value in equation 1.

We will get t = 1/2.

But we have to find how much time it will take after it got slowed.

So total time = 1/2 + 30/60 = 1/2 * 2 = 1 hours;

Friends, we have to use trigonometry to solve this problems. And why they have mentioned average speed is reduced by 200 km/h since it the reduced "speed".

Please tell me the formula of these type of problems.

Flight 1st speed = 600 and due to bad weather average speed = 200 increased by = 30 minutes duration.

200 = 600/(x+30).

200(x+30) = 600.

200x + 6000 = 600.

200x = 600-6000 = 5400

x = 5400/200

x = 27.

x+30 = 27+30 = 57.

Answer: 57 min.

When solving the equation 2x^2+x-3 = 0.

We get two factors for x = 1 and x = -3/2.

Here time is always positive. So we are taking x = 1 there is no logic.

Its simple yeah.

Why because just try think about question.
Any question read at least 2 times.

Ans:

Speed is reduced by 200km per hour.(not reduced to).
So delay extra 30 minutes i.e. in hours 30/60 = 1/2 = 0.5;.
As we know s=d/t; d=600km; without delay time req to reach destination t=T.

So finally,

(600/t) = speed without any delay.
(600/T+0.5) = speed with delay.

From question,
200 = (600/t) - 600/T+0.5).

Then you will get the answer.

Any one solve this simple and shortly? How this x+1/2 came? I'm not getting.

I don't why but this is the second time they have used the difficult method. They use the basic principle to assume the variable to find as x i.e. time of flight as x. I don't follow this always.

Let's do the opposite way. Let us assume the original (or misleadingly called average) speed as x. Now if speed is decreased.

Then the time is increased by 30 mins i.e. 30/60 hrs (since we are using kmph so time has to be in hrs).

Now using common sense logic. If less speed then more time to travel the same distance.

So here the time difference for the two speeds is 30 mins or 30/60 hrs.

i.e (Time with less speed) - (Time with faster speed) = 30/60 hrs.

Now Time = Distance/Speed.

(600/(x-200))-600/x = 30/60.

Solve this equation to get x = 600 kmph.

600 km/600 kmph = 1 hr simple as that.

Just seems lengthy because I explained the logic. But its not always good to assume the unknown as x. This method seems easier to me.

@Ben You are right.

I am just copying a comment listed above.

Let x = original speed.

And y= original time taken.

So 600/x=y-------- (1).

Now we know if speed reduces 30 minutes more will be taken.

i.e 30/60 hours.

So, 600/x-200 = y+30/60 here 30/60 means 30 minutes.

Now put the value of why as shown in (1),

So equation will be, 600/x-200 = 600/x - 30/60.

You will get, x2-200x-240000 = 0 here x2 means x square.

(x-600)(x+200) = 0.

x = 600.

In the above equation we solved x to be 600 where x is the average speed when there isn't any bad weather. But there was bad weather and the flight slowed down to 400 kmph (600kmph-200kmph).

So the time taken for the actual flight due to slow down is 600km/(600kmph-200kmph).

i.e 1 and 1/2 hours.