Raghu and Raman start together to walk a certain equal distance at a speed of 10 km/h and 8 km/h, respectively. Raghu arrives 30 minutes before Raman arrives. Find the distance between the start and the end point.
20 km
Distance Calculation for Walking Speeds
This problem involves calculating a distance based on the speeds of two individuals, Raghu and Raman, and the time difference between their arrivals.
Understanding the Variables
Let's define the key variables and known values:
- Distance to be covered: $d$ (in km)
- Raghu's speed: $v_R = 10$ km/h
- Raman's speed: $v_{Ra} = 8$ km/h
- Time difference: Raghu arrives 30 minutes earlier than Raman.
- Convert time difference to hours: $30 \text{ minutes} = \frac{30}{60} \text{ hours} = 0.5 \text{ hours}$.
- Let $t_R$ be the time taken by Raghu.
- Let $t_{Ra}$ be the time taken by Raman.
We know that Raman takes 0.5 hours longer than Raghu, so:
$$ t_{Ra} - t_R = 0.5 \text{ hours} $$Formulating the Equations
We can use the fundamental relationship between distance, speed, and time: Time = Distance / Speed.
- Time taken by Raghu: $t_R = \frac{d}{v_R} = \frac{d}{10}$ hours.
- Time taken by Raman: $t_{Ra} = \frac{d}{v_{Ra}} = \frac{d}{8}$ hours.
Solving for Distance
Now, substitute the expressions for $t_{Ra}$ and $t_R$ into the time difference equation:
$$ \frac{d}{8} - \frac{d}{10} = 0.5 $$To solve for $d$, we first find a common denominator for the fractions, which is 40:
$$ \frac{5 \times d}{5 \times 8} - \frac{4 \times d}{4 \times 10} = 0.5 $$ $$ \frac{5d}{40} - \frac{4d}{40} = 0.5 $$Combine the fractions:
$$ \frac{5d - 4d}{40} = 0.5 $$ $$ \frac{d}{40} = 0.5 $$Now, multiply both sides by 40 to isolate $d$:
$$ d = 0.5 \times 40 $$ $$ d = 20 $$Therefore, the distance between the start and the end point is 20 km.
Important Questions from Relative Speed
Two trains start from places A and B. respectively, and travel towards each other at the speeds of 60 km/h and 50 km/h. respectively. By the time they meet, the faster train has travelled 110 km more than the slower train. What is the distance between A and B?
A train can cross a tunnel of length 600 m in 54 seconds, and it can cross a 350 m long bridge in 36 seconds. Which of the following statements is/are correct?
(i) The speed of the train is 60 km/h.
(ii) The length of the train is 150 m
A and B started simultaneously and proceeded towards each other from places X and Y, respectively. After meeting each other at a certain point on the way, A and B took 3.2 hours and 1.8 hours, to reach Y and X, respectively. If the speed of B was 12 km/h, then the speed (in km/h) of A was:
Anil started his journey in the morning. Till 10 a.m., he covered \(\frac{1}{2}\) of his journey, and on the same day till 1 a.m., he covered \(\frac{4}{5}\) of his journey. At what time did he start his journey?
Munaf and Surya start simultaneously at the same point on a circular track and run along the track in the same direction. The point on the track at which they meet for the 31st time is the same as that at which they meet for the 43rd time. If the ratio of the speed of the faster boy to that of the slower one is n ∶ 1, where ‘n’ is a natural number, which of the following is NOT a possible value of ‘n’?
