Question

While trekking you could climb with a speed of 2.5 km per hr for the initial distance and while 750 m per hour for the difficult part, If you could reach the peak within 5 hours; how much was the difficult part of the trek, if the peak was 9000 mtr. Away from the foot of the mountain?

Answer 1

Given :

Total distance to cover = 9000 meters

The speed for initial distance = 2.5 km/h = 2500 m/h

The speed for difficult distance = 750 m/h

Total time taken to reach the mountain peak = T = 5 hours

To Find :

Total distance cover in difficult part of trek

Solution :

Let The initial distance cover = x meters

Let The difficult distance cover = (9000 - x) meters

According to question

∵      Time = $\dfrac{Distance}{Speed}$

So,  5 h = $\dfrac{x m}{2500 m/h}$ +  $\dfrac{(9000-x) m}{750 m/h}$

Or   5 =  $\dfrac{3x+ 10(9000-x)}{7500}$

Or,  5 × 7500 = 3 x + 90000 - 10 x

Or,  37500 = 90000 - 7 x

Or,    7 x = 90000 - 37500

Or,    7 x = 52500

∴           x = $\dfrac{52500}{7}$

i.e         x = 7500

So, The initial part of trek = x = 7500 meters

And The difficult part of trek = (9000 - 7500)  = 2500 meters

Hence, The difficult part of trek is 2500 meters  Answer