Question

10. If I had walked 1 km per hr faster, I would have taken 10 mints. Less to walk 2km Find the rate of my walking

Answer 1

Let s = speed of walking
2/s = travel time at speed s
2/(s+1)= travel time at speed (s+1) 
2/s - 2/(s+1) = 1/6 
Simply equation
s^2 + s -12 = 0
(s+4)(s-3) = 0 
s-3 = 0
s=3 
The speed of walking is 3 km/h

Answer 2

Concept: Speed indicates how quickly something or someone is moving. If you know how far something has travelled and how long it took to get there, you can calculate its average speed.

Speed is calculated as follows: speed = distance / time. Knowing the units for distance and time is necessary to calculate the units for speed. The units will be in metres per second (m/s) in this example since the distance is measured in metres (m) and the time is measured in seconds (s).

Given: walked 1km/hr faster

            time taken = 10 min less

             distance = 2km

To find: rate of walking

Solution:

2 kilometres is the distance travelled.

Suppose the starting speed was x km/hr.

$time = \frac{distance}{speed}$

$T_1 = \frac{2}{x}$

Now, the speed is 1 km/hr higher.

$T_2 = \frac{2}{x+1}$

$T_1 - T_2 = 10 min = \frac{10}{60} hr = \frac{1}{6} hr$

Therefore,

$\frac{1}{6} = \frac{2}{x} - \frac{2}{x+1}$

$\frac{1}{6} = 2[\frac{1}{x} - \frac{1}{x+1} ]\\\\\frac{1}{6} = 2[\frac{x+1-x}{x(x+1)} ]\\\\\frac{1}{6} = 2[\frac{1}{x(x+1)}]\\ \\\frac{1}{12} = [\frac{1}{x(x+1)}]\\\\x(x+1) = 12\\\\x^{2} + x -12 = 0\\\\x^{2} +4x - 3x -12 = 0\\\\x(x+4) -3(x+4)=0\\(x+4)(x-3)=0\\x = +3,-4$

Speed cannot be negative.

Speed is thus 3 km/hr.

Hence, rate of walking is 3km/hr

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