Question

Rohan cycles to his office at the rate of 8 km/hr and is late by 6 minutes. However, if he
travels at 12 km/hr, he reaches 4 minutes earlier than the usual time. What is the
distance of his office from his residence?​

Answer 1

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Given:

• Rohan cycles 8km/hr to his office and is late by 6 minutes
• If he travels at 12 km/hr he reaches 4 minutes earlier

To find:

Distance between office and

residence = ?

Solution:

Let x be the distance

$\\ \\ speed \: = \dfrac{distance}{time} \\ \\ time \: = \dfrac{distance}{speed}$

Let t be the time,

While we convert minute into hour we should divide it by 60

6 min = 6/60 hr

4 min = 4/60 hr

For speed 8 km/ hr,

$\\ \\ t = \dfrac{x}{8}$

For speed 12 km/ hr

$\\ \\ t = \dfrac{x}{12}$

Note: We should subtract if we reach early and should add if we reach late

So for 8 km/hr rohan reach late and for 12 km/hr rohan reach early

Let's equate the time,

$\\ \\ \dfrac{x}{8 } + \dfrac{6}{60} = \dfrac{x}{12} - \dfrac{4}{60} \\ \\ \dfrac{x}{8} - \dfrac{x}{12} = \dfrac{ - 4}{60} - \dfrac{ 6}{60} \\ \\ \dfrac{12x - 8x}{96} = \dfrac{ - 10}{60} \\ \\ \dfrac{4x}{96} = \dfrac{ - 10}{60}$

$\\ \\ \dfrac{4x}{96} = \dfrac{ - 1}{6} \\ \\x = \dfrac{ - 96}{24} \\ \\ x = - 4 \: km \\ \\ distance \: cannot \: be \: negative$

$\\ \\ so \: x = 4 \: km$

Answer:

Thus, distance between office and residence is 4 km

Knowledge booster:

• Try to solve such questions with this method only and solve more to get good hold on it