Let t be the number of hours after 8.15am that the lorry
caught up to the van.

Make this chart and put t for the van's time:

          DISTANCE        SPEED        TIME
Van                                      t             
Lorry        

The lorry's time at the instant the lorry caught up is one half
hour less than the van's time, since it started one-half hour
later.  So we put "t-1/2" for the time the lorry traveled before
it caught up the van:


          DISTANCE        SPEED        TIME
Van                                      t             
Lorry                                  t-1/2 

Now we put in the speeds of 50 and 70 km/h:


          DISTANCE        SPEED        TIME
Van                        50            t             
Lorry                      70          t-1/2 

Now we use the formula

                  Distance = (Speed)(Time)

to fill in the two distances:

          DISTANCE        SPEED        TIME
Van         50t            50            t             
Lorry     70(t-1/2)        70          t-1/2 


The two distances were equal at the instant when the 
lorry caught up.  So

    50t = 70(t-1/2)

Can you solve that for t?

Answer: t = 1 3/4 hours.

That is, an hour and 45 minutes after 8.15am, 
which would be 10.00am.

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(b) If the lorry reached Town Y at 1.45pm, what 
is the distance between the 2 towns?

Let d = the distance between the 2 towns.

The lorry started at 8.45am (one half hour after 8.15am) 
and reached town Y at 1.45pm.  That is 5 hours.  The 
speed of the lorry was 70 km/hr.

  Use distance = speed times time.

             d = 70(5)
             d = 350 km.

Edwin