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Arun drove from home to his hostel at 60 miles per hour. While returning home he drove half way along the same route at a speed of 25 miles per hour and then took a bypass road which increased his driving distance by 5 miles, but allowed him to drive at 50 miles per hour along this bypass road. If his return journey took 30 minutes more than his onward journey, then the total distance traveled by him is
  • a)
    55 miles
  • b)
    60 miles
  • c)
    65 miles
  • d)
    70 miles
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Arun drove from home to his hostel at 60 miles per hour. While returni...
Ans.

Option (c)

Let distance from home to hostel be d.
Time taken to go from home to hostel = d/60
Time taken to drive at 25 miles from hostel to home = d/25
Time to drive through bypass = (d/2 + 5)/50
Total time taken from hostel to home = d/25 + (d/2 + 5)/50
According to the question,
d/25 + (d/2 + 5)/50 = d/60 + 30/60 (Convert time from minutes to hours)
On solving, we get d = 30
Total distance travelled = 2d + 5 = 65miles
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Most Upvoted Answer
Arun drove from home to his hostel at 60 miles per hour. While returni...
Given:
- Distance from home to hostel = x miles
- Speed while going from home to hostel = 60 miles per hour
- Speed while returning = 25 miles per hour for half the distance, then 50 miles per hour for the remaining distance + 5 miles
- Return journey took 30 minutes more than onward journey

To find:
The total distance traveled by Arun

Solution:

Let's assume that the distance from home to hostel is x miles.

Distance covered in the onward journey = x miles
Time taken in the onward journey = Distance / Speed = x / 60 hours

Distance covered in the return journey = (x/2) + (x/2 + 5) miles
Time taken in the return journey = Distance / Speed = (x/2) / 25 + (x/2 + 5) / 50 hours

Given that the return journey took 30 minutes more than the onward journey, we can write the equation as:

Time taken in the onward journey + 30 minutes = Time taken in the return journey
(x / 60) + (30/60) = (x/2) / 25 + (x/2 + 5) / 50

Simplifying the equation:

(x/60) + 0.5 = (x/50) + (x/100) + (5/50)
(x/60) - (x/50) - (x/100) = (5/50) - 0.5
[(5x - 6x - 3x)/300] = [5 - 25]/50
-4x/300 = -20/50
-4x/300 = -2/5

Cross-multiplying, we get:
5 * -4x = -2 * 300
-20x = -600
x = 600 / 20
x = 30

Therefore, the total distance traveled by Arun is:
Distance = x + (x/2 + x/2 + 5) = 30 + (15 + 15 + 5) = 30 + 35 = 65 miles

Hence, the correct answer is option C) 65 miles.
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Arun drove from home to his hostel at 60 miles per hour. While returning home he drove half way along the same route at a speed of 25 miles per hour and then took a bypass road which increased his driving distance by 5 miles, but allowed him to drive at 50 miles per hour along this bypass road. If his return journey took 30 minutes more than his onward journey, then the total distance traveled by him isa)55 milesb)60milesc)65milesd)70milesCorrect answer is option 'C'. Can you explain this answer?
Question Description
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