A person X from a place A and another person Y from a place B set out at the same time to walk towards each other. The places are separated by a distance of 15 km. X walks with a uniform speed of 1.5 km / hr and Y walks with a uniform speed of 1 km / hr in the first hour, with a uniform speed of 1.25 km / hr in the second hour and with a uniform speed of 1.5 km / hr in the third hour and so on. Which of the following is / are correct? 1. They take 5 hours to meet. 2. They meet midway between A and B. Select the correct answer using the code given below:
Both 1 and 2
Given:
Distance between place A and place B = 15 km.
Speed of X = 1.5 km/hr and is uniform
Speed of Y = 1 km/hr in the 1 st hour, 1.25 km/hr in the 2 nd hour, 1.5 km/hr in the 3 rd hour and so on..
Calculation:
Solving it by using relative velocity method approach with respect to X.
As both X and Y are moving towards each other so relative velocity of X and Y will add up.
For the first hour,
Relative velocity = 1.5 + 1 = 2.5 km/hr
time = 1 hr
Distance travelled = 2.5 × 1 = 2.5 km. Similarly,a
Time (hr) | Relative Velocity (km/hr) | Distance travelled(km) | Cummulative Distance(km) | |||
| For the first hour | 1 | 1.5 + 1 = 2.5 | 2.5 | 2.5 | ||
| In the second hour | 1 | 1.5 + 1.25 = 2.75 | 2.75 | 5.25 | ||
| In the third hour | 1 | 1.5 + 1.5 = 3 | 3 | 8.25 | ||
| In the fourth hour | 1 | 1.5 + 1.75 = 3.25 | 3.25 | 11.50 | ||
| In the fifth hour | 1 | 1.5 + 2 = 3.5 | 3.5 | 15 |
So, after 5 hours they will meet. Statement 1 is correct
Now as they both travelled for 5 hours. So distance travelled by
- X = 1.5 × 5 = 7.5 km
- Y = 15 - 7.5 = 7.5 km
Hence, they will meet in the middle. Statement 2 is correct
So, option 3 is correct.
Important Questions from Partial Speed
A train having length 210 metres takes 25 seconds to cross a 540 metres long bridge. How much time will the train take to cross a 630 metres long bridge?
The speed of a train is 120 kmph. What is the distance covered by it in 15 minutes?
I walk a certain distance and ride back taking a total time of 37 minutes. I could walk both ways in 55 minutes. How long would it take me to ride both ways ?
Karan had covered two third of a certain distance when his car had a breakdown. He parked it and covered the remaining distance on foot. His time of travel on foot was 9 times his time of travel on car. What is the ratio of his walking speed with respect to his car’s speed?
Two runners finish a 20 km marathon race in a difference of 30 mins. What is the winner's speed if their speeds differ by 2 km/h?
