Winnie drives from A to B, a distance of 40km, at an average speed of x km per hour. For the return journey she averages 20km per hour faster. Given that the total journey must be completeed within an hour and she does not at any time exceed the speed limit of 80km per hour, find x.
I need help on the last part, don't get what 'she does not at any time exceed the speed limit of 80km per hour' means.

Question

Winnie drives from A to B, a distance of 40km, at an average speed of x km per hour. For the return journey she averages 20km per hour faster. Given that the total journey must be completeed within an hour and she does not at any time exceed the speed limit of 80km per hour, find x.
I need help on the last part, don't get what 'she does not at any time exceed the speed limit of 80km per hour' means.

anonymous · Answer

@hartnn @phi @ganeshie8 @AravindG any help?

ganeshie8 · Answer

average value of speed for entire trip = 80km/1 hour = 80kmph

ganeshie8 · Answer

and max speed = 80 kmph

ganeshie8 · Answer

thats the hypothesis

anonymous · Answer

So it would go on the right side of the equation then after the $\leq$ ?

ganeshie8 · Answer

hmm she needs to maintain the max speed all the time, if she wants to complete the trip in 1 hour.

ganeshie8 · Answer

For the return journey she averages 20km per hour faster is JUST FALSE.

@hartnn

anonymous · Answer

Would that mean her speeds in the journey and return are $\leq$ 80kmph?

ganeshie8 · Answer

she has to maintain 80 kmph.
she cannot go below that... 

cuz u ave 40 + 40 = 80 km to travel
u need to maintain 80kmph speed to complete the journey in 1hour

ganeshie8 · Answer

GIVEN THAT U CANNOT GO BEYOND 80kmph

anonymous · Answer

So 80kmph exactly?

anonymous · Answer

So can you check my equation?

ganeshie8 · Answer

there is a problem wid the question :-

Winnie drives from A to B, a distance of 40km, at an average speed of x km per hour. For the return journey she averages 20km per hour faster. Given that the total journey must be completeed within an hour and she does not at any time exceed the speed limit of 80km per hour, find x.

@phi @hartnn  can u have a look if not bze :)

anonymous · Answer

How is there a problem?

anonymous · Answer

I don't get it sorry...

phi · Answer

40km, speed of x  
using speed * time= distance,  time= distance/speed
here time_1= 40/x

returning, speed is  20km per hour faster, or 20+x
time_2= 40/(x+20)


 completeed within an hour
means the sum of the time going and returning must be 1 hour or less.

$$ t_1 + t_2 ≤ 1 \ \frac{40}{x}+\frac{40}{x+20} ≤ 1 $$

speed limit of 80km means x+20 ≤ 80  or x≤60 km/hr

However there is a problem. if we go x=60 , and return at x= 60+20= 80, the total time is
$$ \frac{40}{60}+ \frac{40}{80} \ \frac{2}{3} + \frac{1}{2}= \frac{7}{6} $$
which is longer than 1 hour.

In other words, for this problem, you cannot complete the trip in one hour, with out speeding.

anonymous · Answer

But this question has an answer?