Question

A man has to reach a certain place in a certain time.
if he walks 3km an hour he is 10 minutes late and if
4km
an hour he is 5 mins early Find the distance
he has to walk​

Answer 1

Answer:

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