Question

A clerk walks from his house at 4km/h and reaches his office 5 minutes late. If
his speed is 5Km/h, he will reach his office 10 minutes early. How far is his office
from home?​

Answer 1

Distance = Speed*Time

Change speed to km per minute by dividing by 60.

Let t be the time it would take if he arrived exactly on time.

Set up two equations for distance using the two given situations.

d = (4/60)(t+5) = (t+5)/15

d = (5/60)(t-10)= (t-10)/12

Set equations equal and solve for t:

15(t-10) = 12(t+5)

15t - 150 = 12t + 60

3t = 210

t = 70

Finally, substitute t back into one of the equations for d:

d = (70+5)/15 = 75/15 = 5

The office is 5 km from his house.

**Additional Note:

Given this distance, you can also find the ideal speed to walk to arrive at the office in exactly 70 minutes.

Let v be ideal speed.

d = v*t

v = d/t = 5/70 = 1/14

Multiply by 60 to convert back to km per hour.

v = 60/14 ~ 4.3 km/hr

Answer 2

Let the distance be x km.

$\frac{x}{4} - \frac{x}{5} = \frac{15}{60} \\ \\ \huge\boxed {\boxed{\boxed{x = 5km}}}$