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Vimla starts for office every day at 9am and reaches on time if she drives at her usual speed 40km/hr she is late by 6 minute if she drive 35km/hr one day she covers two third of her distance to office in one third of her usual time to reach office and then stop for 8 minute the speed in km/hr at which she should drive the remaining distance to reach office exactly on time is?
Verified Answer
Vimla starts for office every day at 9am and reaches on time if she dr...
Let the time taken with its usual speed = x
So the distance that she covers = 40x
Now 40x = 35*(x + 6/60) = 35x + 3.5
5x = 3.5
Or x = 0.7 hrs = 42 min
So distance = 40x = 40*0.7 = 28 km
As per question, she covers 2/3 rd of distance in 1/3rd time that is 56/3 km in 42/3 = 14 min
She took rest for 8 min so total time remains = 42 – 8 – 14 = 20 min
And she need to cover = 28 – 56/3 = 28/3 km
So required speed = (28/3)/(20/60) = 28 kmph
This question is part of UPSC exam. View all CAT courses
Most Upvoted Answer
Vimla starts for office every day at 9am and reaches on time if she dr...
Given information:
- Vimla starts for office every day at 9am
- If she drives at her usual speed of 40km/hr, she is late by 6 minutes
- When she drives at 35km/hr, she covers two-thirds of her distance in one-third of her usual time to reach the office
- After covering two-thirds of her distance, she stops for 8 minutes
To find:
The speed at which Vimla should drive the remaining distance to reach the office exactly on time
Solution:
Let's break down the problem into steps to find the solution.
Step 1: Find the usual distance to the office
To find the usual distance to the office, we need to know the usual time it takes for Vimla to reach the office at her usual speed.
Let's assume the usual time taken by Vimla to reach the office at her usual speed of 40km/hr is 't' hours.
Distance = Speed × Time
Distance = 40 × t
Let's denote the usual distance as 'D'.
D = 40t
Step 2: Find the time taken to cover two-thirds of the distance at 35km/hr
From the given information, we know that when Vimla drives at 35km/hr, she covers two-thirds of her distance in one-third of her usual time.
Let's assume the time taken by Vimla to cover two-thirds of the distance at 35km/hr is 't1' hours.
Distance covered = Speed × Time
Distance covered = 35 × t1
According to the given information, t1 = (1/3)t
Step 3: Find the remaining distance to the office
The remaining distance to the office after covering two-thirds of the distance can be calculated as:
Remaining distance = Total distance - Distance covered
Remaining distance = D - (2/3)D
Remaining distance = (1/3)D
Step 4: Find the time taken to cover the remaining distance at the required speed
To find the required speed at which Vimla should drive the remaining distance to reach the office exactly on time, we need to know the time taken to cover the remaining distance.
Let's assume the required speed is 'v' km/hr and the time taken to cover the remaining distance at this speed is 't2' hours.
Distance covered = Speed × Time
Distance covered = v × t2
According to the given information, t2 = (1/3)t1 + 8 minutes
Step 5: Find the required speed
To find the required speed at which Vimla should drive the remaining distance to reach the office exactly on time, we need to equate the time taken to cover the remaining distance at the required speed with the usual time taken.
v × t2 = t
Substituting the values of t2 and t1, we get:
v × [(1/3)t1 + 8/60] = t
v × [(1/3)(1/3)t + 8/60] = t
v × [(1/9)t + 8/60] = t
v × (1/9)t + v × 8/60 = t
Simplifying the equation, we get:
(v
- Vimla starts for office every day at 9am
- If she drives at her usual speed of 40km/hr, she is late by 6 minutes
- When she drives at 35km/hr, she covers two-thirds of her distance in one-third of her usual time to reach the office
- After covering two-thirds of her distance, she stops for 8 minutes
To find:
The speed at which Vimla should drive the remaining distance to reach the office exactly on time
Solution:
Let's break down the problem into steps to find the solution.
Step 1: Find the usual distance to the office
To find the usual distance to the office, we need to know the usual time it takes for Vimla to reach the office at her usual speed.
Let's assume the usual time taken by Vimla to reach the office at her usual speed of 40km/hr is 't' hours.
Distance = Speed × Time
Distance = 40 × t
Let's denote the usual distance as 'D'.
D = 40t
Step 2: Find the time taken to cover two-thirds of the distance at 35km/hr
From the given information, we know that when Vimla drives at 35km/hr, she covers two-thirds of her distance in one-third of her usual time.
Let's assume the time taken by Vimla to cover two-thirds of the distance at 35km/hr is 't1' hours.
Distance covered = Speed × Time
Distance covered = 35 × t1
According to the given information, t1 = (1/3)t
Step 3: Find the remaining distance to the office
The remaining distance to the office after covering two-thirds of the distance can be calculated as:
Remaining distance = Total distance - Distance covered
Remaining distance = D - (2/3)D
Remaining distance = (1/3)D
Step 4: Find the time taken to cover the remaining distance at the required speed
To find the required speed at which Vimla should drive the remaining distance to reach the office exactly on time, we need to know the time taken to cover the remaining distance.
Let's assume the required speed is 'v' km/hr and the time taken to cover the remaining distance at this speed is 't2' hours.
Distance covered = Speed × Time
Distance covered = v × t2
According to the given information, t2 = (1/3)t1 + 8 minutes
Step 5: Find the required speed
To find the required speed at which Vimla should drive the remaining distance to reach the office exactly on time, we need to equate the time taken to cover the remaining distance at the required speed with the usual time taken.
v × t2 = t
Substituting the values of t2 and t1, we get:
v × [(1/3)t1 + 8/60] = t
v × [(1/3)(1/3)t + 8/60] = t
v × [(1/9)t + 8/60] = t
v × (1/9)t + v × 8/60 = t
Simplifying the equation, we get:
(v
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Vimla starts for office every day at 9am and reaches on time if she drives at her usual speed 40km/hr she is late by 6 minute if she drive 35km/hr one day she covers two third of her distance to office in one third of her usual time to reach office and then stop for 8 minute the speed in km/hr at which she should drive the remaining distance to reach office exactly on time is?
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Vimla starts for office every day at 9am and reaches on time if she drives at her usual speed 40km/hr she is late by 6 minute if she drive 35km/hr one day she covers two third of her distance to office in one third of her usual time to reach office and then stop for 8 minute the speed in km/hr at which she should drive the remaining distance to reach office exactly on time is? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Vimla starts for office every day at 9am and reaches on time if she drives at her usual speed 40km/hr she is late by 6 minute if she drive 35km/hr one day she covers two third of her distance to office in one third of her usual time to reach office and then stop for 8 minute the speed in km/hr at which she should drive the remaining distance to reach office exactly on time is? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Vimla starts for office every day at 9am and reaches on time if she drives at her usual speed 40km/hr she is late by 6 minute if she drive 35km/hr one day she covers two third of her distance to office in one third of her usual time to reach office and then stop for 8 minute the speed in km/hr at which she should drive the remaining distance to reach office exactly on time is?.
Vimla starts for office every day at 9am and reaches on time if she drives at her usual speed 40km/hr she is late by 6 minute if she drive 35km/hr one day she covers two third of her distance to office in one third of her usual time to reach office and then stop for 8 minute the speed in km/hr at which she should drive the remaining distance to reach office exactly on time is? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Vimla starts for office every day at 9am and reaches on time if she drives at her usual speed 40km/hr she is late by 6 minute if she drive 35km/hr one day she covers two third of her distance to office in one third of her usual time to reach office and then stop for 8 minute the speed in km/hr at which she should drive the remaining distance to reach office exactly on time is? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Vimla starts for office every day at 9am and reaches on time if she drives at her usual speed 40km/hr she is late by 6 minute if she drive 35km/hr one day she covers two third of her distance to office in one third of her usual time to reach office and then stop for 8 minute the speed in km/hr at which she should drive the remaining distance to reach office exactly on time is?.
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