Question

A person starts walking at a speed of 5 km/hr through half the distance, rest of the distance he covers with a speed 4km/hr. Total time of travel is 9 hours. What is the maximum distance he can cover?

Answer 1

Answer:

ans = 40

Explanation:

let distance = x

then time taken in first half  = x/2*5 = x/10

and time taken in 2nd half = x/2*4 = x / 8

given total time = 9 hours

then  x/10 + x/8 = 9

x=40

Answer 2

Maximum distance the person can cover = 40 km

Given :

• A person starts walking at a speed of 5 km/hr through half the distance, rest of the distance he covers with a speed 4 km/hr.

• Total time of travel is 9 hours

To find :

The maximum distance the person can cover

Solution :

Step 1 of 2 :

Form the equation to calculate the distance

Let the maximum distance the person can cover = 2d km

According to the question, the person walks d km at a speed of 5 km/hr and covers d km with a speed 4 km/hr

∴ Total time of travel

$\displaystyle \sf = \bigg( \frac{d}{5} + \frac{d}{4} \bigg) \: \: hours$

$\displaystyle \sf = \bigg( \frac{4d + 5d}{20} \bigg) \: \: hours$

$\displaystyle \sf = \frac{9d}{20} \: \: hours$

So by the given condition

$\displaystyle \sf \frac{9d}{20} = 9$

Step 2 of 2 :

Calculate maximum distance the person can cover

$\displaystyle \sf \frac{9d}{20} = 9$

$\displaystyle \sf{ \implies }d = 9 \times \frac{20}{9}$

$\displaystyle \sf{ \implies }d = 20$

Hence maximum distance the person can cover

= 2d km

= (2 × 20) km

= 40 km

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