If Ram walks from his house at 5 kmph, he reaches school 10 min early, and if he walks at 4 kmph he reaches it 5 min late. What is the actual distance

Question

If Ram walks from his house at 5 kmph, he reaches school 10 min early, and if he walks at 4 kmph he reaches it 5 min late. What is the actual distance between Ram's house and his school?

Answer 1

Another way to look at it:

 

distance = rate*time

Let t = time in hours to arrive 10 mins early.

Difference in time is 15 mins or 1/4 hours more to arrive 5 mins late

 

d = 5(t)  

d = 4(t + 1/4)

 

5t = 4(t + 1/4)

5t = 4t + 1

t = 1

 

d = 5t = 5(1) = 5 km

Answer 2

Let t = # of hours to arrive exactly on time. 10 min early is 1/6 hour early; 5 min late is 1/12 hour late.

Now we write the distance as product of a rate and a particular time:

 

5 km/hr•(t-1/6)hr = 4 km/hr•(t+1/12)hr

 

5t -5/6 = 4t + 1/3  or t = 5/6 + 2/6 = 7/6 hour, or 70 minutes for just-on-time arrival.

 

Thus the distance is 5(7/6 - 1/6) = 5 km.