Question

Ravi is expected to reach his office at 8.30 AM. He started from his house at an average speed of 6 km/h and
reached his office at 9.00 AM. Next day he started 5 minutes earlier than the previous day and travelled at an
average speed of 8km/h and reached his office at 8.30 AM. What is the distance of his office from his house?​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The distance between Ravi's office and his house is 10 km.

• The time at which Ravi is required to reach to his office is 8:30 am. There are two cases and two different days of travel from his house to his office.
• In the first case he starts from his house at a particular time and reaches his office at 9:00 am travelling with a speed given to be 6 km/hr.
• Since he is supposed to be in the office by 8:30 but instead reaches at 9 am and hence the amount time he is late by is 30 minutes, because if he had reached 30 mins earlier he would have been at his office at 8:30 am.
• We need to assume the time at which he started from his house in both the cases here, because it is not given.
• For easier calculation and time tracking we take the time at which he started to be 8:00 am in the first case which means that the minute hand and is at 12 exactly and the hour hand is at 8 exactly when he starts from his house.
• He reaches at 9:00 am and hence the minute hand is at 12 while the hour hand would have moved to 9 on the clock.
• This means that the minute hand would have traversed one whole revolution and 60 minutes have passed.
• The time taken by Ravi to travel the distance from home to office with 6 km/hr speed will hence be 1 hour in the first case.
• Similarly, in the second case he leaves 5 minutes earlier which means that he would have left at 7:55 am as we our assumption is that he leaves at 8 am the previous day.
• He is said to reach at 8:30 am with a speed of 8 km/hr which means that 35 minutes would have passed.

We need to find the difference in the time on both the days to find the amount of time he is late by. Thus we have:

$\Delta T=T_1-T_2$ ---------(1)      

where, $T_1$ is the time taken on the first day

$T_2$ is the time taken on the second day

$\implies \Delta T=(60-35)\;min$

$\implies \Delta T=25\;min$

We know that the speed, distance time formula is given as:

$T=\frac{D}{S}$ ------------------(2)

where,

T is the time taken

D is the distance

S is the speed

Hence, we can say that from equation (1) and (2) we have:

$\Delta T=\frac{D_1}{S_1}-\frac{D_2}{S_2}$

Here, the distances in both cases are the same as in both these days Ravi's travels from his house to the office which would be the same.

Since, $D_1=D_2=D$ and speeds are given as 6 km/hr and 8 km/hr respectively we have:

$\Delta T=\frac{D}{6}-\frac{D}{8}$

We also found out that $\Delta T=25\;min$ and by substituting this we have:

$\frac{D}{6}-\frac{D}{8}=25$

The 25 minutes is converted to hours by dividing with 60. Hence we have:

$\implies \frac{8D-6D}{48}=\frac{25}{60}$

On solving the equation we get:

$\implies \frac{D}{24}=\frac{25}{60}$

$\implies D=\frac{24\times 5}{12}$

$\implies D=10 km$

Thus, the distance between Ravi's office to his house is 10 km.

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