Question

From home, Rajan rides on his motorbike at 35 km/hr and reaches his office 5 minutes
late. If he had ridden at 50 km/hr, he would have reached his office 4 minutes earlier. How far
is his office from his home?
Solution:​

Answer 1

• The distance to his office = 17 1/2 km

Step-by-step explanation:

Let,

• The distance be 'd' km
• Time taken to cover 'd' km = T1 = x / 35 hrs
• Time taken to cover 'd' km = T2 = x / 50 hrs

Formula,

• Time = Distance / Speed

We know that,

• Speed 1 = 35 km / hr
• Speed 2 = 50 km / hr

According to the question,

⟼ Difference between timings = 4 - (-5)

⟼ 4 + 5

⟼ 9 minutes

• Changing minutes to hours = 9 / 60 hr.

Finding Distance,

⟼ T1 - T2 = 9 / 60

⟼ (x / 35) - (x / 50) = 9 / 60

⟼ 10x - 7x / 350 = 9 / 60

⟼ 3x / 350 = 9 / 60

⟼ x = (9 / 60) × (350 / 3)

⟼ x = 17 1/2 km.

• The distance to his office = 17 1/2 km.

Answer 2

Answer:

Distance between Rajan's home and office is 17½ Km.

Step-by-step explanation:

Given that :

• At 35 km/hrs. speed, Rajan reaches 5 min late
• At 50 km/hrs. speed, Rajan reaches 4 min earlier

To find :

• Distance between office and home

Solution :

• Let, the distance between office and home be s Km.
• Let, correct time of reaching the office from home be t hrs.

Case 1 :

• When Rajan drives at 35 Km/hrs. he reaches office 5 min. late.
• Converting 5 min into hours, we get;
• 5 min = 5/60 hrs. = 1/12 hrs.
• Total time taken by Rajan to reach office is
• t1 = (t + 1/12)hrs.
• Distance covered by Rajan is

$s = 35(t + \frac{1}{12} ) \: km \: \: - - - (1)$

Case 2 :

• When Rajan drives at 50 Km/hrs. he reaches office 4 min. earlier.
• Converting 4 min into hours, we get;
• 4 min = 4/60 hrs. = 1/15 hrs.
• Total time taken by Rajan to reach office is
• t2 = (t - 1/15)hrs.
• Distance covered by Rajan is

$s = 50(t - \frac{1}{15} ) \: \: - - - (2)$

• From equation (1) and (2), we get;

$35(t + \frac{1}{12} ) = 50(t - \frac{1}{15} ) \\ 35t + \frac{35}{12} = 50t - \frac{50}{15} \\ 15t = \frac{35}{12} + \frac{50}{15} \\ 15t = \frac{175 + 200}{60} \\ 15t = \frac{375}{60} \\ t = \frac{375}{60 \times 15} \\ t = \frac{25}{60} \\ t = \frac{5}{12} hrs$

• Correct time taken to reach office is 5/12 hrs
• Distance between home and office is

$s = 35( \frac{5}{12} + \frac{1}{12} ) \: \: \: by \: equation(1) \\ s = 35 \times \frac{6}{12} \\ s = \frac{35}{2} \\ s = 17 \frac{1}{2} km$

• Hence, distance between home and office is 17½ km.