Question

if a scooterist drives at a rate of 24km/hr.from his home.he reaches his work place 5 minutes late.but if he drives at a rate of 30km/he.he reaches his work place 4 minutes early.find the distance of his work place and home​

Answer 1

Solution :

let the distance of work place from home be x km

Case I :

speed of scooterist = 24 km/hr

let the time taken be t_1 hour

speed = distance/time

24 = x/t_1

t_1 = x/24

Case II ;

speed of scooterist = 30 km/hr

let the time taken be t_2 hour

speed = distance/time

30 = x/t_1

t_1 = x/30

ATQ :

t_1 - t_2 = 9 minutes = 9/60 hours

x/24 - x/30 = 9/60

5x - 4x/120 = 9/60

x = 9 x 120/60

x = 9 x 2

x = 18 km

=> the distance of his work place and home of scooterist is 18

Answer 2

Answer:

✡ Question ✡

➡ If a scooterist drives at a rate of 24km/hr.from his home.he reaches his work place 5 minutes late.but if he drives at a rate of 30km/he.he reaches his work place 4 minutes early.find the distance of his work place and home.

✡ Given ✡

⚫ Scooterist drives at a rate of 24km/hr

⚫ He drives at a rate of 30km/hr

✡ To Find ✡

➡ The distance of his work place and home.

✡ Formula Used ✡

▶ Speed = $\dfrac{distance}{time}$

✡ Solution ✡

➡ Let the distance of work place from home be x km

$\text{\large\underline{\pink{Case\: 1}}}$

✏ Speed of the Scooterist is 24km/hr

✏ Let the time taken be $\sf{t_1}$ hours

✍ Speed = $\dfrac{distance}{time}$

=> 24 = $\dfrac{x}{t_1}$

=> $\sf{t_1}$ = $\dfrac{x}{24}$

$\text{\large\underline{\green{Case\: 2}}}$

✏ Speed of the Scooterist is 30km/hr

✏ Let the time taken be $\sf{t_2}$ hours

✍ Speed = $\dfrac{distance}{time}$

=> 30 = $\dfrac{x}{t_1}$

=> $\sf{t_1}$ = $\dfrac{x}{30}$

According to the question,

=> $\dfrac{x}{t_1}$ - $\dfrac{x}{t_2}$ = 9min => $\dfrac{9}{60}$ hours

=> $\dfrac{x}{24}$ - $\dfrac{x}{30}$ = $\dfrac{9}{60}$

=> $\dfrac{5x-4x}{120}$ = $\dfrac{9}{60}$

=> x = $\dfrac{9×120}{60}$

=> x = 9×2

=> x = $\bold{\huge{\fbox{\color{blue} {18 km}}}}$

∴ The distance of his work place and home or scooterist is 18km.

Step-by-step explanation:

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