SOLUTION: Cyclist A started his journey on cycle at 7:30 a.m. at a speed of 8 km/h. After 30 minutes, cyclist B started from the same place but with a speed of 10 km/h. At what time did B ov

(The other tutor added 2 hours to 7:30am and got 9:30am. He should
have added it to 8:00am to get 10:00am.)


First let's do it in our heads without algebra, 
then we'll do it with algebra:

In our heads:

When B starts at 8am, A has been going 8 km/h for half an hour, so A
has a 4 km head start on B.  B then chases A going 2 km/h faster 
than A, so B is approaching A at 2 km/h.  At that catch-up rate it will 
take B 2 hours to make up A's 4 km head start.  So B will overtake A 
at 10am.

By algebra.

Let t be the time it takes B to overtake A

Make this chart

     Distance     Rate    Time 
A
B

Fill in t for B's time

     Distance     Rate    Time 
A
B                          t

A's time is a half hour longer than B's time
since he started half an hour sooner, so fill in
t+.5 for A's time:

     Distance     Rate    Time 
A                         t+.5
B                          t

Their rates are given so fill those in:

     Distance     Rate    Time 
A                  8      t+.5
B                 10       t

Now use  to
fill in the distances:

     Distance     Rate    Time 
A     8(t+.5)      8      t+.5
B      10t        10       t

They traveled the same distance so the
two distances are equal:

   8(t+.5) = 10t
      8t+4 = 10t
         4 = 2t
         2 = t

B started half an hour later than 7:30am, or
8am.  2 hours later it will be 10am. 

Edwin