I do not understand the logic behind the solution to this question, please help

[1vam0]

I know the solution and how this problem is solved but don't know why it is done in that particular way, here is the question :

A walks at a uniform rate of 4
km an hour; and 4 hours after
his start, B bicycles after him at
the uniform rate of 10 km an
hour. How far from the starting
point will B catch A ?

The solution is to find the distance A travels in 4 hours , which is 4x4 km = 16 km, A has travelled 16km before B can start
Next the relative speed of A and B is obtained whichis 10-4 = 6 km per hour
I do not understand the next step, relative time = 16km / 6 kmph= 2.67 hr
and finally the B catches A at a distance of 10kmph x 2.67hr = 26.7 km from the starting point,

can anyone please explain this as I am unable to visualize it

Thank you

 

[lev888]

Do you understand what relative speed is?

 

[Harry_the_cat]

Here's another way to think about it.

After 4 hours A has travelled 16km.

Let h be the time (in hours) it takes for B to catch up. Distance = speed x time

Total distance travelled by A = 16 + 4h
Total distance travelled by B = 10h

So 16 + 4h = 10h which gives h = 2.67 hours (approx) etc

 

[Jagulba]

see if you can follow this figure

 

[HallsofIvy]

A walks at a uniform rate of 4
km an hour; and 4 hours after
his start, B bicycles after him at
the uniform rate of 10 km an
hour. How far from the starting
point will B catch A ?

The first part, multiplying 4 km an hour by 4 hours, to get 16 km, calculates the distance between A and B when B starts. The speed of B "relative to" A is 10- 4= 6 km an hour. That is, if we were to imagine A stopped, B would be moving toward him at 6 km an hour. It will take 16 km/6 km an hour= 8/3 hour.

Another way to do this: Take t to be the time, in hours, after B starts until B catches A. Since A is walking at 4 km an hour, he will have gone 4t km in that time. Since B is bicycling at 10 km an hour, he will have gone 10t km. Since B starts 16 km behind A, when B catches A, 10t= 4t+ 16. The first thing you would do to solve that is subtract 4t from both sides: 10t- 4t= 6t= 16. That is exactly what we did when we got the "relative speed" of 6 km an hour.

 

[1vam0]

Thank you all for your time and valuable help. I understand now

I understood it once I saw this method:

Here's another way to think about it.

After 4 hours A has travelled 16km.

Let h be the time (in hours) it takes for B to catch up. Distance = speed x time

Total distance travelled by A = 16 + 4h
Total distance travelled by B = 10h

So 16 + 4h = 10h which gives h = 2.67 hours (approx) etc

see if you can follow this figure

View attachment 13425

thanks for the pictorial help,