Question

if a person travels at the speed of 30 km/h, then he reaches his destination 10 minutes late, while traveling at the speed of 42 km/h, he reaches his destination 10 minutes before. The distance traveled by a person is:​

Answer 1

let :-

• Time taken by the person = x hours

To Find :-

• Distance travelled by the person = ?

Solution :-

• To calculate the distance travelled by the person at first we have to set up equation with the help of given clue in the question.

Calculation begins :-

• Data as per 1st case :-

⇒ Speed = 30km/h. Time = (x + 10/60) hours

⇒ Distance = Speed × Time

⇒ Distance = 30(x + 10/60)

• Data as per 2nd case

⇒ Speed = 42km/h. Time = (x - 10/60) hours

⇒ Distance = Speed × Time

⇒ Distance = 42(x - 10/60)

⇒ As per case - (i) = As per case - (ii)

⇒ 30(x + 10/60) = 42(x - 10/60)

⇒ 30x + 300/60 = 42x - 420/60

⇒30x + 5 = 42x - 7

⇒ 42x - 30x = 5 + 7

⇒ 12x = 12

⇒ x = 1

Hence,

Distance travelled by the person = 30(x + 10/60)

⇒ 30(1 + 10/60)

⇒ 30(60+10/60)

⇒30 × 70/60

⇒ 35km

Answer 2

Given:-

if a person travels at the speed of 30 km/h, then he reaches his destination 10 minutes late, while traveling at the speed of 42 km/h, he reaches his destination 10 minutes before.

To find:-

The distance traveled by a person..

Solution:-

Let the actual time taken to reach the destination by man be x

Case 1: If speed of man, u=30 km/h

He reaches his destination 10 minute late..

$\sf \pink{Example:}$ Distance between man & destination point, S=speed of man × Time taken..

Main Point:-

10 min=$\dfrac{10}{60}$ =$\dfrac{1}{6}$

So,

S=30×(Time+$\dfrac{1}{6})$. [$\sf \pink{Step 1:}]$

Case 2: If speed of man v=42km/h, he reaches his destination 10 minutes early..

$\sf \pink{Example:}$ Distance between man & destination point, S=speed of man × Time taken..

=42×(Time-$\dfrac{1}{6})$km [$\sf \pink{Step 2:}]$

Now, from equations (1) & (2),

30(Time+$\dfrac{1}{6})$=42(Time-$\dfrac{1}{6})$

Therefore 10 T+$\dfrac{10}{6}$=14 T-$\dfrac{14}{6}$

Therefore $\dfrac{10}{6}$+$\dfrac{14}{6}$=14 T-10 T

Therefore $\dfrac{24}{6}$=4 T

Or Time= 1 hour..

By putting T in $\sf \pink{Step 1}$

S=30(1+$\dfrac{1}{6})$=30×$\dfrac{7}{6}$=35 km

________________

Hence, the distance traveled is 35 km..