Question

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

Answer 1

The Correct Option is C

To solve this problem, we need to calculate the total distance Arun traveled. Let's denote the one-way distance from home to the hostel as \(D\) miles.

Step 1: Calculate Time for Onward Journey
Arun's speed from home to hostel was 60 miles/hour. Therefore, the time taken for the onward journey is:

\(t_1 = \frac{D}{60}\) hours

Step 2: Calculate Time for Return Journey
For the return journey, Arun drove half the distance (i.e., \(\frac{D}{2}\) miles) at 25 miles/hour, and the remaining distance (i.e., \(\frac{D}{2}+5\) miles) at a speed of 50 miles/hour on the bypass road.

Time for the first half:
\(t_2 = \frac{D/2}{25} = \frac{D}{50}\) hours
Time for the bypass road:
\(t_3 = \frac{(D/2)+5}{50}\) hours

Total time for the return journey:
\(T_{\text{return}} = t_2 + t_3 = \frac{D}{50} + \frac{(D/2)+5}{50} = \frac{D}{50} + \frac{D}{100} + \frac{5}{50}\)

Simplifying:
\(T_{\text{return}} = \frac{2D}{100} + \frac{D}{100} + \frac{1}{10} = \frac{3D}{100} + \frac{1}{10}\)

Step 3: Use Given Information
According to the problem, the return journey took 30 minutes (or \(\frac{1}{2}\) hour) longer than the onward journey:

\(\frac{3D}{100} + \frac{1}{10} = \frac{D}{60} + \frac{1}{2}\)

Step 4: Solve the Equation
Multiply through by 300 to clear the fractions:

And simplifying:

\(9D + 30 = 5D + 150\)

\(4D = 120\)

\(D = 30 \) miles

Step 5: Calculate Total Journey
Total distance traveled equals the distance to and from the hostel, accounting for the bypass:

Total distance = \(D + \left(\frac{D}{2} + \frac{D}{2} + 5\right) = 30 + 35 = 65 \) miles

Therefore, the total distance traveled by Arun is 65 miles.