Question

if I drive at a speed of 24 km per hour ., I reach 5 minutes late and if I drive at 30km per hour , I reach 4 minutes too soon . Find the distance of the school from my residence (in kilometres)
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Answer 1

Answer :

Distance covered by you from your home to school is 18 km.

Explanation :

Let distance covered by you from your home to school be " d " km.

Let actual time taken be " x "

We know that,

Distance = speed × time

According to Question,

d = 24 ( x + 5/60 )_____________(1)

d = 30 ( x - 4/60 )_____________(2)

Equating (1) and (2),

24 ( x + 5/60 ) = 30 ( x - 4/60 )

=> 24x + 2 = 30x - 2

=> 24x - 30x = - 2 - 2

=> - 6x = -4

=> x = 2/3

Put x = 2/3 in (1),

=> d = 24 [ (2/3) + (5/60) ]

=> d = 24 [ 9/12 ]

=> d = 2 × 9

=> d = 18 km

•°• Distance covered by you from your home to school is 18 km.

Answer 2

$\huge\bold\green{Question}$

If I drive at a speed of 24 km per hour . I reach 5 minutes late and if I drive at 30km per hour , I reach 4 minutes too soon . Find the distance of the school from my residence (in kilometres).

$\huge\bold\blue{AnsWer}$

Let the duration that he will be on time be “ x ” hour

Case - 1

• If i drive at speed of 24 km/h

$\sf\green{Distance = Speed x Time}$

$\implies\sf{24 \: x + \frac{5}{60} } \\ \\ \implies\sf{24\: x + \frac{1}{12} }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀__________ (1) eqn

Case - 2

• If i drive at speed of 30 km/h

$\sf\green{Distance = Speed x Time}$

$\implies\sf{30 \: x - \frac{4}{60} } \\ \\ \implies\sf{30 \: x - \frac{1}{15} }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀____________(2)eqn

By comparing eqn (1) and (2) , we get :-

$\sf{24\: x + \frac{1}{12} } \: = \sf{30 \: x - \frac{1}{15} }$

$\sf{24x + 2 = 30x - 2}$

$\sf{30x - 24x = 2 + 2} \\ \sf{6x = 4}$

$\sf \green{x = \frac{2}{3} \: hours }$

Now , we find the distance , By putting the value of “ x ” in eqn (1) we get ,

$\sf{distance = 24\: ( \frac{2}{3} + \frac{1}{12})}$

$\large \sf \red{distance = 18 \: km} \:$